4.73   ODE No. 1073

\[ \boxed { {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) +{\frac { \left ( 11\,{\it WeierstrassP} \left ( x,a,b \right ) {\it WeierstrassPPrime} \left ( x,a,b \right ) -6\, \left ( {\it WeierstrassP} \left ( x,a,b \right ) \right ) ^{2}+a/2 \right ) {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) }{{\it WeierstrassPPrime} \left ( x,a,b \right ) + \left ( {\it WeierstrassP} \left ( x,a,b \right ) \right ) ^{2}}}+{\frac { \left ( \left ( {\it WeierstrassPPrime} \left ( x,a,b \right ) \right ) ^{2}- \left ( {\it WeierstrassP} \left ( x,a,b \right ) \right ) ^{2}{\it WeierstrassPPrime} \left ( x,a,b \right ) -{\it WeierstrassP} \left ( x,a,b \right ) \left ( 6\, \left ( {\it WeierstrassP} \left ( x,a,b \right ) \right ) ^{2}-a/2 \right ) \right ) y \left ( x \right ) }{{\it WeierstrassPPrime} \left ( x,a,b \right ) + \left ( {\it WeierstrassP} \left ( x,a,b \right ) \right ) ^{2}}}=0} \]

  1. Problem in Latex
  2. Mathematica input
  3. Maple input

Mathematica: cpu = 1.365173 (sec), leaf count = 129 \[ \text {DSolve}\left [\frac {y'(x) \left (-\wp (x;a,b) \wp '(x;a,b)+\wp (x;a,b)^3-6 \wp (x;a,b)^2+\frac {a}{2}\right )}{\wp '(x;a,b)-\wp (x;a,b)^2}+\frac {y(x) \left (\wp (x;a,b)^2 (-\wp '(x;a,b))-\left (6 \wp (x;a,b)^2-\frac {a}{2}\right ) \wp (x;a,b)+\wp '(x;a,b)^2\right )}{\wp (x;a,b)^2+\wp '(x;a,b)}+y''(x)=0,y(x),x\right ] \]

Maple: cpu = 2.511 (sec), leaf count = 109 \[ \left \{ y \left ( x \right ) ={\it DESol} \left ( \left \{ {\frac { {\rm d}^{2}}{{\rm d}{x}^{2}}}{\it \_Y} \left ( x \right ) +{\frac {{ \frac {\rm d}{{\rm d}x}}{\it \_Y} \left ( x \right ) }{{\it WeierstrassPPrime} \left ( x,a,b \right ) + \left ( {\it WeierstrassP} \left ( x,a,b \right ) \right ) ^{2}} \left ( 11\,{\it WeierstrassP} \left ( x,a,b \right ) {\it WeierstrassPPrime} \left ( x,a,b \right ) -6 \, \left ( {\it WeierstrassP} \left ( x,a,b \right ) \right ) ^{2}+{ \frac {a}{2}} \right ) }+{\frac {{\it \_Y} \left ( x \right ) }{{\it WeierstrassPPrime} \left ( x,a,b \right ) + \left ( {\it WeierstrassP} \left ( x,a,b \right ) \right ) ^{2}} \left ( \left ( {\it WeierstrassPPrime} \left ( x,a,b \right ) \right ) ^{2}- \left ( {\it WeierstrassP} \left ( x,a,b \right ) \right ) ^{2}{\it WeierstrassPPrime } \left ( x,a,b \right ) -{\it WeierstrassP} \left ( x,a,b \right ) \left ( 6\, \left ( {\it WeierstrassP} \left ( x,a,b \right ) \right ) ^{ 2}-{\frac {a}{2}} \right ) \right ) } \right \} , \left \{ {\it \_Y} \left ( x \right ) \right \} \right ) \right \} \]