
    wg0                     D   d dl mZmZmZ d dlmZmZmZ d dlm	Z	 d dl
mZmZ d dlmZmZ d dlmZ d dlmZmZ d dlmZmZmZ d d	lmZ d d
lmZmZ d dlmZm Z  d dl!m"Z"m#Z#  ed      \  Z$Z%Z&Z'Z( edd      \  Z)Z*Z+Z, ed      Z- ed      Z. ed      Z/e#d        Z0d Z1y)    )
DerivativeFunctiondiff)IRationalpi)Eq)Symbolsymbols)explog)sqrt)cossin)Eierferfi)Integral)checkodesolchecksysodesol)besseljbessely)raisesslowzC0:5zu,x:zT)realfghc                     t        t        d        t        t        d        t        t        t              j                  t              t        t        t        t              t                    dt        t              j                  t               t        t        t              j                  t              z   dz
  fk(  sJ t        t        t              j                  t              t        t        t              t                    dusJ t        t        t              j                  t              t        t        t              t                    dk(  sJ t        t        t              dz  dt        t              z  z   d	t        t              z  z
  t        z   d
      } t        t        | j                  t              |       dk(  sJ t        t        | j                  t              t        t        t                    z  |       dk(  sJ t        t        | j                  t        d	      |       dk(  sJ t        t        | j                  t        d	      t        t        t                    z  |       dk(  sJ t        t        | j                  t        d      |       dk(  sJ t        t        | j                  t        d      t        t        t                    z  |       dk(  sJ t        t        | j                  t        d      t        t        t              t        t        t              z              ddt        dz  z  t        t              dz   d	z  t        t              z   z  t        t              dz   z  t        t              d	z  z  dt        dz  z  t        t              dz  z  z
  dz
  fk(  sJ t        t        t        t        t                    t        z   t              t        z  t        t        t        t                    t        z   d
            dk(  sJ t        t        t        t        t                    t        z   t              t        z  t        t        t        t                    t        z   d
      d      dk(  sJ t        t        t              j                  t        d	      t        t        t              t        t        t        z  z         t        t        t              t        t        t        z  z         t        t        t              t        t        z  t        t        d	z  z  z         g      dddt        fgk(  sJ t        t        t              j                  t        d	      t        t        t              t        t        t        z  z         t        t        t              t        t        t        z  z         t        t        t              t        t        z  t        t        d	z  z  z         h      dddt        fhk(  sJ t        t        t              j                  t              dt        t              z  d	z  z
  t        t        t              d	z  t                    ddgk(  sJ t        t        t              j                  t              t        t              z
  t        t        t        t              z  t        t                          dk(  sJ t        t        t        t              t        z        z  t        t              z   t        t        t              j                  t              z  z
  }t        t        t              t        t        t        t        z        t         z              }t        ||      d   j                  t        t                    rJ t        t        t        t        t        t              t              z  t              t        z  t        t                    }t        t        t              t        t        t        t              z  z   t        t              z   t        t              z
        }t        ||d	d      d
   sJ t        d	z  t        t              j                  t        d	      z  t        t        t              j                  t              z  z   d	t        d	z  z  dz   t        t              z  z   }t        t        t              t        t!        dt"        z  t%        d	      t        z        z  t        t'        dt"        z  t%        d	      t        z        z  z         }t        ||      dk(  sJ t        t        t              j                  t              t        t              t)        t              z         t        t)        t              j                  t              t        t              t)        t              z         g}t        t        t              t         t        t        d	t        z        z  z         t        t)        t              t        t        t        d	t        z        z  z         g}t        ||      dd
d
gfk(  sJ y )Nc            	          t        t        t        t              j	                  t              t        t        t        t              t                    S N)r   r   xyr   r	        k/home/mcse/projects/flask/flask-venv/lib/python3.12/site-packages/sympy/solvers/ode/tests/test_subscheck.py<lambda>z"test_checkodesol.<locals>.<lambda>   s'    {1Q7<<?BqAwNK r%   c            	          t        t        t              j                  t              t	        t        t        t
              t              t        t        t
                    S r!   )r   r   r"   r   r	   r#   r$   r%   r&   r'   z"test_checkodesol.<locals>.<lambda>   s4    {1Q499Q<AaG:Aw  r%   F   T)Fr)            r   )Tr      <      	   )solve_for_func)orderr1      )r   
ValueErrorr   r   r"   r   r	   r#   lhsr   r   C1C2hasr   r   r   r   r   r   r   )sol1eq3sol3eqnsoleqeqss          r&   test_checkodesolr@      s    :KL
:  qtyy|R!Q^4	11!QQ/!345 5 5qtyy|R!a[1===qtyy|R!a[1Z???adAg1Q4!AaD&(1,a0DtDHHa($/9<<<tDHHa(QqT2D9YFFFtDHHa+T2i???tDHHa+C!I5t<	IIItDHHa+T2i???tDHHa+C!I5t<	IIItDHHa+R!aAh-?@	1a4#a&1*q3q612A
FAI !!Q$s1vqy 01345 	66 6 6 tC!IM1-a/C!IM11EF  tC!IM1-a/C!IM11E!*+ + +qtyyAAaD"r!t))<
1Q4bdR!bdR1Wn5)7 8	Ir{+, , , qtyyAAaD"r!t))<
1Q4bdR!bdR1Wn5)7 8	Ir{+, , , qtyy|a!fQh.1Q47A?	I  qtyy|ad*Br#a&y!A$,?@IMMM C!QK-!A$
1Q499Q<
/CadCBqD	QB()D3%a(,,QqT222
Z*QqT1--q1!3SV
<C
QqT23q6	>CF*RU2
3CsCq?BBB	
AqtyyA	!QqTYYq\"2	2a1fbj!A$5F	FB
QqT2gac4719--71Q3Q	3J0JJ
KCr39,,,adiilAaD1Q4K("QqTYYq\1Q4!A$;*G
HCadRC"S1X+%&1Q4bQqSk1A(B
CCsC TAq6N222r%   c                  H   t        dt              \  } }}t        d      }t        t	         | |      |      d ||      z        t        t	         ||      |      d | |      z        f}t         | |      dt
        z  t        dt        d      z  |z        z  dt        z  t        dt        d      z  |z        z  z         t         ||      dt        d      z  t
        z  t        dt        d      z  |z        z  dt        d      z  t        z  t        dt        d      z  |z        z  z         g}t        ||      d	d
d
gfk(  sJ t        t	         | |      |      d | |      z  d ||      z  z         t        t	         ||      |      d | |      z  d ||      z  z         f}t         | |      dt
        z  t        |t        d       dz  t        dd      z   z        z  dt        z  t        |t        d      dz  t        dd      z   z        z  z         t         ||      t
        t        d       dz  t        dd      z   z  t        |t        d       dz  t        dd      z   z        z  t        t        dd      t        d      dz  z   z  t        |t        d      dz  t        dd      z   z        z  z         g}t        ||      d	d
d
gfk(  sJ t        t	         | |      |       | |       ||      z         t        t	         ||      |      d | |      z  d ||      z  z         f}t         | |      t
        t        t        d      |z  dz        z  t        t        t        d      |z  dz        z  z   t        |t        dd      z        z        t         ||      t
        dz  t        d      t        z  dz  z
  t        t        d      |z  dz        z  t        d      t
        z  dz  t        dz  z   t        t        d      |z  dz        z  z   t        |t        dd      z        z        g}t        ||      d	d
d
gfk(  sJ t        t	         | |      |       | |       ||      z   dz         t        t	         ||      |      d | |      z  d ||      z  z   dz         f}t         | |      t
        t        |t        d       dz   z        z  t        t        |t        d      dz   z        z  z   t        dd      z
        t         ||      t
        t        d       dz   z  t        |t        d       dz   z        z  t        dt        d      z   z  t        |t        d      dz   z        z  z   t        dd      z
        g}t        ||      d	d
d
gfk(  sJ t        t	         | |      |       | |       ||      z   dz         t        t	         ||      |      d | |      z   ||      z   dz         f}t         | |      t
        t        t        d      |z        z  t        t        t        d      |z        z  z   t        |      z  t        dd      z
        t         ||      t        d      t
        z  t        t        d      |z        z  t        d      t        z  t        t        d      |z        z  z
  t        |      z  t        dd      z
        g}t        ||      d	d
d
gfk(  sJ t        t	         | |      |      d|z   | |      z  d ||      z  z         t        t	         ||      |      d | |      z  d|z   ||      z  z         f}t         | |      t
        t        t        d|      j                               z  t        t        t        d|      j                                z  z   t        t        d|z  |      j                               z        t         ||      t
        t        t        d|      j                               z  t        t        t        d|      j                                z  z
  t        t        d|z  |      j                               z        g}t        ||      d	d
d
gfk(  sJ t        t	         | |      |      d|z   | |      z  |dz   ||      z  z         t        t	         ||      |      |dz    | |      z  d|z   ||      z  z         f}t         | |      t
        t        t        |dz  |      j                               z  t        t        t        |dz  |      j                               z  z   t        t        d|z  |      j                               z        t         ||      t
         t        t        |dz  |      j                               z  t        t        t        |dz  |      j                               z  z   t        t        d|z  |      j                               z        g}t        ||      d	d
d
gfk(  sJ t        t	         | |      |      d|z   | |      z  |dz   ||      z  z         t        t	         ||      |      |dz    | |      z  d|z  d|dz  z  z    ||      z  z         f}t         | |      t
        t        t        d       dz  t        dd      z   t        |dz  |      j                         z        z  t        t        t        d      dz  t        dd      z   t        |dz  |      j                         z        z  z   t        t        d|z  |      j                               z        t         ||      t
        t        d       dz  t        dd      z   z  t        t        d       dz  t        dd      z   t        |dz  |      j                         z        z  t        t        d      dz  t        dd      z   z  t        t        d      dz  t        dd      z   t        |dz  |      j                         z        z  z   t        t        d|z  |      j                               z        g}t        ||      d	d
d
gfk(  sJ t        t	         | |      ||      d | |      z  d ||      z  z         t        t	         ||      ||       | |      d ||      z  z         f}t        t        d       dz          }t        t        d       dz         }t        t        d      dz          }t        t        d      dz         }	t         | |      dt
        z  t        ||z        z  dt        z  t        ||z        z  z   dt        z  t        ||z        z  z   dt         z  t        ||	z        z  z         t         ||      t
        |dz  dz
  z  t        ||z        z  t        |dz  dz
  z  t        ||z        z  z   t        |dz  dz
  z  t        ||z        z  z   t         |	dz  dz
  z  t        ||	z        z  z         g}t        ||      d	d
d
gfk(  sJ t        t	         | |      ||      d | |      z  d ||      z  z   dz         t        t	         ||      ||      d | |      z  d ||      z  z   dz         f}t        t        d       dz  t        dd      z          }t        t        d       dz  t        dd      z         }t        t        d      dz  t        dd      z          }t        t        d      dz  t        dd      z         }	t         | |      dt
        z  t        ||z        z  dt        z  t        ||z        z  z   dt        z  t        ||z        z  z   dt         z  t        ||	z        z  z   t        dd       z
        t         ||      t
        |dz  dz
  z  t        ||z        z  t        |dz  dz
  z  t        ||z        z  z   t        |dz  dz
  z  t        ||z        z  z   t         |	dz  dz
  z  t        ||	z        z  z   t        d!d       z         g}t        ||      d	d
d
gfk(  sJ t        t	         | |      ||      dt	         ||      |      z  z
  d | |      z  z   d
      t        t	         ||      ||      dt	         | |      |      z  z   d ||      z  z   d
      f}t         | |      t
        t        |t        dd      t        d      dz  z   z        z  t        t        |t        dd      t        d      dz  z   z        z  z   t        t        |t        d       dz  t        dd      z   z        z  z   t         t        |t        d       dz  t        dd      z   z        z  z         t         ||      t
         t        |t        dd      t        d      dz  z   z        z  t        t        |t        dd      t        d      dz  z   z        z  z   t        t        |t        d       dz  t        dd      z   z        z  z
  t         t        |t        d       dz  t        dd      z   z        z  z         g}t        ||      d	d
d
gfk(  sJ t        t	         | |      ||      d|z  t	         ||      |      z  d ||      z  z
        t        t	         ||      ||      d|z  t	         | |      |      z  d | |      z  z
        f}t        d      dt        d"d      z  z  t        t"              z  t%        t        d      dt        d"d      z  z  |z  dz        z  dz  t        dt        d      z  |dz  z  dz        |z  z
  }
t        d       dt        d"d      z  z  t        t"              z  t'        t        d      dt        d"d      z  z  |z  dz        z  dz  t        d#t        d      z  |dz  z  dz        |z  z
  }t         | |      t        |z  |dt
        z  |
z  dt        z  |z  z   z  z         t         ||      t         |z  |dt        d      z  t
        z  |
z  dt        d      z  t        z  |z  z
  z  z         g}t        ||      d	d
d
gfk(  sJ t        t	         | |      |      d$ | |      z        t        t	         ||      |      d% | |      z  d ||      z  z         t        t	         ||      |      d | |      z  d ||      z  z   d ||      z  z         f}t         | |      t
        t        d$|z        z        t         ||      d%t
        z  t        d$|z        z  d&z  t        t        d|z        z  z         t         ||      d't
        z  t        d$|z        z  d(z  dt        z  t        d|z        z  dz  z
  t        t        d|z        z  z         g}t        ||      d	g d)fk(  sJ t        t	         | |      |      d ||      z  d* ||      z  z
        t        t	         ||      |      d ||      z  d | |      z  z
        t        t	         ||      |      d* | |      z  d ||      z  z
        f}t         | |      dt(        z  t        d+      t
        z  t        t        d+      |z        z  z   dt
        z  dz  d,t        z  dz  z   t        t        d+      |z        z  z         t         ||      d*t(        z  t        d+      t        z  t        t        d+      |z        z  z   d-t
        z  dz  dt        z  dz  z
  t        t        d+      |z        z  z         t         ||      dt(        z  t        d+      d.t
        z  dz  d*t        z  dz  z
  z  t        t        d+      |z        z  z   d*t
        z  dt        z  z
  t        t        d+      |z        z  z         g}t        ||      d	g d)fk(  sJ t        dt	         | |      |      z  d/ ||       ||      z
  z        t        dt	         ||      |      z  d ||       | |      z
  z        t        dt	         ||      |      z  d | |       ||      z
  z        f}t         | |      t(        dt        d      z  t
        z  t        dt        d      z  |z        z  z   dt
        z  dz  d0t        z  dz  z   t        dt        d      z  |z        z  z         t         ||      t(        dt        d      z  t        z  t        dt        d      z  |z        z  z   d1t
        z  d2z  dt        z  dz  z
  t        dt        d      z  |z        z  z         t         ||      t(        dt        d      z  d3t
        z  d4z  d5t        z  d4z  z
  z  t        dt        d      z  |z        z  z   dt
        z  dz  dt        z  dz  z
  t        dt        d      z  |z        z  z         g}t        ||      d	g d)fk(  sJ t        t	         | |      |      d | |      z   ||      z
        t        t	         ||      |      d | |      z  d ||      z  z    ||      z
        t        t	         ||      |      d | |      z   ||      z         f}t         | |      t
        t        d|z        z  t        |z  t        d|z        z  z   t        t        d|z        z  z   t        |dz  z  t        d|z        z  dz  z   t        |z  t        d|z        z  z   t        t        d|z        z  z         t         ||      t
        t        d|z        z  t        |z  t        d|z        z  z   t        t        d|z        z  z   t        |dz  z  t        d|z        z  dz  z   t        |z  t        d|z        z  z         t         ||      dt
        z  t        d|z        z  dt        z  |z  t        d|z        z  z   t        t        d|z        z  z   t        |dz  z  t        d|z        z  z   t        |z  t        d|z        z  z   t        t        d|z        z  z         g}t        ||      d	g d)fk(  sJ t        t	         | |      |      d | |      z   ||      z
  d ||      z  z
        t        t	         ||      |      d | |      z   ||      z   d ||      z  z
        t        t	         ||      |      d | |      z  d ||      z  z
        f}t         | |      t
        t        d|z        z  t        t        |       dt        |      z  z   z  z   t        dt        |      z  t        |      z   z  z         t         ||      t        t        |       dt        |      z  z   z  t        dt        |      z  t        |      z   z  z         t         ||      t
        t        d|z        z  dt        z  t        |      z  z   dt        z  t        |      z  z         g}t        ||      d	g d)fk(  sJ t        t	         | |      |       | |       ||      dz  z        t        t	         ||      |       ||      dz        f}t         | |      t
        t        d6dt        z  d|z  z   z  t        d6d      z        z        t         ||      d6dt        z  d|z  z   z  t        d"d      z         t         | |      t
        t        d6d6dt        z  d|z  z   z  t        d"d      z  z        z        t         ||      d6dt        z  d|z  z   z  t        d"d      z        t         | |      t
        t        t*         d6dt        z  d|z  z   z  t        d"d      z  z        z        t         ||      t*         d6dt        z  d|z  z   z  t        d"d      z  z        t         | |      t
        t        t*        d6dt        z  d|z  z   z  t        d"d      z  z        z        t         ||      t*        d6dt        z  d|z  z   z  t        d"d      z  z        g}t        ||      d	d
d
gfk(  sJ t        t	         | |      |      t        d | |      z         ||      dz  z        t        t	         ||      |       ||      dz        f}t         | |      t-        t
        dd6dt        z  d|z  z   z  t        d"d      z  z  z
         dz        t         ||      d6dt        z  d|z  z   z  t        d"d      z         t         | |      t-        t
        dd6dt        z  d|z  z   z  t        d"d      z  z  z          dz        t         ||      d6dt        z  d|z  z   z  t        d"d      z        t         | |      t-        t
        dt*        z  d6dt        z  d|z  z   z  t        d"d      z  z  z          dz        t         ||      t*         d6dt        z  d|z  z   z  t        d"d      z  z        t         | |      t-        t
        dt*        z  d6dt        z  d|z  z   z  t        d"d      z  z  z
         dz        t         ||      t*        d6dt        z  d|z  z   z  t        d"d      z  z        g}t        ||      d	d
d
gfk(  sJ t         | |      |t	         | |      |      z  t	         | |      |      t	         ||      |      z  z         t         ||      |t	         ||      |      z  t	         ||      |      dz  z         f}t         | |      t
        t        z  t
        |z  z         t         ||      t        dz  t        |z  z         h}t        ||      d	d
d
gfk(  sJ y )7Nzx, y, z)clstr0      ir-      Tr   r,   r/   )   i  +   '      r*         Q   :      M   /         m               r)                  )r   r   r   r+         ii      i
   ir3      )r   r   r
   r	   r   r6   r   r   r7   r   r   r   r   r   doitC3C4r   r   r   C0r   r   )r"   r#   zrC   r>   r=   root0root1root2root3I1I2s               r&   test_checksysodesolrq   M   s}"   iX.GAq!sA
T!A$q\1QqT6
"BtAaD|R!W$=	>BadAbDRQZ\**QrT#aQik2B-BBCqtRQZ]3r$q'z!|,,qay|C$q'	!<L/LLMOC"c"taVn444
T!A$q\1QqT6AadF?
+RQqT!b1g1Q4>O-P	QBadAbDQdAQ ?@AAAbDQPTUYPZ[\P\ROQ N J E  1Q4d4j[]Xb!_%D!Ec!dSWj[YZ]RON K G "HROd4jl:;C4:a<RZ[]_`RaCa@b<cc"d efC "c"taVn444
T!A$q\1Q4!A$;
'D1aL"QqT'AadF:J)K	LBadRDGAIaK((2c$q'!)A+.>+>>AhqRSnDT@UUVqtr!td1gbjl"CQ	!$44Q
1qD9	
d1gaik
8 (1a. 012 34C "c"taVn444
T!A$q\1Q4!A$;?
+RQqT!a!fq1voPR>R-S	TBadBs1tAwhl+,,r#aa1o2F/FFRO 1rDG8a<0Qa15E1FFQGN JDGaK!J"  "$,QN 3 45C "c"taVn444
T!A$q\1Q4!A$;+
,bad1r!A$w1~PR?R.S	TBadRDGAI&CQ	N)::CFBXbRS_TUqtd1gbjT!WQY'$q'"*Sa^*CCSVKhWZ\]N^^_aC"c"taVn444
T!A$q\1Q3qt8a!f,
-r$qtA,!A$1QqT@Q/R	SBadRHQN//122Rhq!n=R=R=T<T8U5UU!A#q	!"# $%'!r#x1~6K6K6M2N/NsXa^!!##$$0%&)8AaC+;*A*A*C&D/E &FGC "c"taVn444
T!A$q\1Q3qt8ad1Q4i/
0"T!A$q\AqD51:PQRSPSTUVWTXPXCX2Y	ZBadRXadA.44677"S(1a4QRBSAYAYA[=\:\\!A#q	!"# $%'!s3Aq8I7O7O7Q3R/RsHQT1##%&&0'(+Xac1-=,C,C,E(F/G &HIC "c"taVn444
T!A$q\1Q3qt8ad1Q4i/
0"T!A$q\AqD51:QRSTQTUVWXZ[W[U[Q[]^_`]aPaCa2b	cBadRd2hYq[8Aq>9HQT1<M;S;S;UUVVsDHQJ!Q'(1a4*;)A)A)CCDDEFI8TUVWTWYZK[JaJaJcFde fqtb48)A+A./d2hYq[8Aq>5QT\]^`a]acdTeSkSkSm4m0nnR
Xa^#$S$r(1*x1~*EQRTUQUWXHYG_G_Ga)a%bbcdgiqrsturuwxiyhh  iB  eCC DEC "c"taVn444
T!A$q^QqtVb1g-
.4!Qq>1Q4!AaD&=0Q	RB48)a-  E$r(QE$r(Q,EbAEadBrE#ag,&Bs1U7|);;beC%L>PPSUVXSXY\]^_d]dYeSeefqtRAs1U7|+b%(Q,.?AeG.LLq1c!E'l"#%'A%6s1U7|%CD EFC "c"taVn444
T!A$q^QqtVAadF]2-
.4!Qq>1QqT6!AaD&=QSCS0T	UB49*Q,"a011E$s)AQ/0E$s)A+Q/00Ec1xA./EadAbDQuW%"S5\(99AbDQuW<MMPQRTPTUXYZ[`Y`UaPaadlmprtduuvqtRAs1U7|+b%(Q,.?AeG.LLq1c!E'l"#%'A%6s1U7|%CDFNsTVFWX YZC "c"taVn444
T!A$q^aQqT!n,q1v5a
8"T!A$q^aPTUVWXUYZ[P\n=\_`abcdae_e=efg:h	iBadBs1hq!ntCy{:;<<r#aRSUVZ^_bZcdeZeIeFfBg?ggs1tCyjlXa^+,--.023q49*Q,RSUV:W7X3Y0YZ [\^_`ab_cfhehilmnpxyz|}p~  BF  GJ  BK  LM  BM  qM  nN  jO  fOQAc1,-	..f/13CDI:a<(STVW.;X8Y4Z1Zf[]_`cdehlmphqgqrsgsv~  @A  CD  wE  hE  eF  aG  ^GfG ]HIC "c"taVn444
T!A$q^QqSad1-a!f4
5r$qtAa.1TRSTURVWX\IYZ[\]^_\`Z`I`7a	bB	aHQN"	"48	+DaHQN9J1J11LQ1N,O	OPQ	QTWXYZ^_`ZaXabcefbfXfghXhTijkTk	kB
q'!Xa^#	#DH	,SaHQN9J1J11LQ1N-O	OPQ	QTWXZ[_`a[bXbcdfgcgXghiXiTjklTl	lBadBqD1ad2g"R/0012adBqD1aQiPRlSUoXYZ^_`ZaXabdXdegXgFgCh<h3i
jC"c"taVn444
T!A$q\2ad7
#RQqT!b1ga!fn%Er$qQRtTU,XYZ[\]Z^X^_`abcdae_eXefghijkhlflXlGm	nBadBs2a4yL!2adBrE#bd)OB,>C!H,L#MqtSVC1Ic!AbDQqSM!O3bQqSkABDC"c"tY&7777
T!A$q\!AaD&AaD.
)"T!A$q\!AaD&1Q4-*HDQRSTQUVWLY[\]^_\`Y`abcdefcgagYgIh	iBadAbD49R<DIaK(888BrE!Gc"fQh<NPSTXY\T]^_T_P`;``aqtRUT#Yr\#d3ik"222c"fQhBq6H#dSViXYkJZ5ZZ[qtQrTDIr"uQwBq01#d3ik2BBBbeaPRdlTWX\]`XabcXcTdEddegC "c"tY&7777
QtAaD|^C1adO
,R$qtA,sAaD1I-OPRSTUYZ[\]Z^_`UaSabeghijgklmnolpgpbqPr	sBadB472c!DG)A+&666"R%'CF2I:MsSTUYZ[U\S\]^S^O_9__`qtR!DG)B,s1T!W9Q;///3r6"9r"uQw3FAdSTgIVWKHX2XXYqtR!DG)RU2X2b01#aQik2BBBbeAgPRSUPUVWPWFWY\]^_cde_f]fgh]hYiEiijlC "c"tY&7777
T!A$q\!AaD&1Q4-
(D1aL1Q4!A$qt9K)LRPTUVWXUYZ[P\]^_`ab_c]cdefgdh]hMi	jBadBs1Q3xK"Q$s1Q3x-/"S1X+=1a4AaC@PQR@RRUWXYUYZ]^_`a^aZbUbbeghklmnolohpeppqqtRAaC[2a4AaC=(2c!A#h;6AqDQqS9I!9KKbQRdSVWXYZWZS[m[\qtQrT#ac(]QrT!VC!H_,r#ac({:R1WS1X=MMPRSTPTUXYZ[\Y\U]P]]`bcfghijgjck`kklnC "c"tY&7777
T!A$q\!AaD&1Q4-!AaD&0
1"T!A$q\!AaD&1Q4-QRSTUVSWQWBW2XY[\`abcdaefg\hijklmnkoiopqrsturvpvivYw	xBadBs1Q3xK"s1vg#a&&8"99B#a&3q6@Q<RRSqtR#a&1SV8#$r1SV8c!f+<'==>1Q4CPQRSPSHWXY[W[\_`a\bWbIbefgieijmnojpepIp@qsC"c"tY&7777
T!A$q\!A$qtQw,
'D1aL1q)A	BBadBsB"qs
OxA?@@A2adbRSTVRVYZ[\Y\R\o`hijlm`nMnLnCoqtRBAbD1Q3J(1a.8899:Bqtb!B$QRSTQT*oX`abdeXfEf<gqtRQBAbD1Q3J(1a.8899:BqtaRQrTTUVWTWZ[cdegh[iHiEi<jqtRAr1R4!A#:!Q778892adAr1R4RSTURU:YabcefYgFgDg;hjC "c"taVn444
T!A$q\3q1v;qtQw.
/4!Q<1q0I	JBadSaQrTAaCZ8Aq> AAABB1DEr!A$RTVWXZVZ]^_`]`V`RadlmnpqdrQrPrGsqtc"q"adQqSj/HQN:::;;A=>1Q4"aPRdUVWXUXj/\defhi\jIj@kqtc"qsB"qs
Ohq!n<<<==a?@"QqTA2rSTUWSWZ[\]Z]S]aijkmnaoNoKoBpqtc"qsB"qs
Ohq!n<<<==a?@"QqT1bRSTVRVYZ[\Y\R\o`hijlm`nMnKnBoqC "c"taVn444
QqT!D1aL.ad1d1Q4l!::
;R!QtAaDQR|^TXYZ[\Y]^_T`bcTcEc=d	eBadBrEBqDL!2adBEBqDL#9
:C"c"taVn444r%   N)2sympy.core.functionr   r   r   sympy.core.numbersr   r   r   sympy.core.relationalr	   sympy.core.symbolr
   r   &sympy.functions.elementary.exponentialr   r   (sympy.functions.elementary.miscellaneousr   (sympy.functions.elementary.trigonometricr   r   'sympy.functions.special.error_functionsr   r   r   sympy.integrals.integralsr   sympy.solvers.ode.subscheckr   r   sympy.functionsr   r   sympy.testing.pytestr   r   ri   r6   r7   rg   rh   ur"   r#   rj   r   r   r   r@   rq   r$   r%   r&   <module>r      s    < < 0 0 $ / = 9 ? C C . C , - V_ BBW4(
1aSMSMSM 03 03f~5r%   