5.28   ODE No. 1476

\[ \boxed { 27\,{\frac {{\rm d}^{3}}{{\rm d}{x}^{3}}}y \left ( x \right ) -36\,{n}^{2}{\it WeierstrassP} \left ( x,{\it g2},{\it g3} \right ) {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) -2\,n \left ( n+3 \right ) \left ( 4\,n-3 \right ) {\it WeierstrassPPrime} \left ( x,{\it g2},{\it g3} \right ) y \left ( x \right ) =0} \]

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

Mathematica: cpu = 0.128516 (sec), leaf count = 44 \[ \text {DSolve}\left [-36 n^2 y'(x) \wp (x;\text {g2},\text {g3})-2 (n+3) (4 n-3) n y(x) \phi '(x)+27 y^{(3)}(x)=0,y(x),x\right ] \]

Maple: cpu = 0.234 (sec), leaf count = 62 \[ \left \{ y \left ( x \right ) ={\it DESol} \left ( \left \{ 27\,{\frac { {\rm d}^{3}}{{\rm d}{x}^{3}}}{\it \_Y} \left ( x \right ) -36\,{n}^{2}{ \it WeierstrassP} \left ( x,{\it g2},{\it g3} \right ) {\frac {\rm d}{ {\rm d}x}}{\it \_Y} \left ( x \right ) + \left ( -8\,{\it WeierstrassPPrime} \left ( x,{\it g2},{\it g3} \right ) {n}^{3}-18\,{ \it WeierstrassPPrime} \left ( x,{\it g2},{\it g3} \right ) {n}^{2}+18\, n{\it WeierstrassPPrime} \left ( x,{\it g2},{\it g3} \right ) \right ) { \it \_Y} \left ( x \right ) \right \} , \left \{ {\it \_Y} \left ( x \right ) \right \} \right ) \right \} \]