6.9   ODE No. 1542

\[ \boxed { {\it d4y} \left ( x \right ) +a{\it WeierstrassP} \left ( x,{\it g2},{\it g3} \right ) {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) +b{\it WeierstrassPPrime} \left ( x,{\it g2},{\it g3} \right ) {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) + \left ( c \left ( 6\, \left ( {\it WeierstrassP} \left ( x,{\it g2},{\it g3} \right ) \right ) ^{2}-{\it g2}/2 \right ) +d \right ) y \left ( x \right ) =0} \]

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

Mathematica: cpu = 0.029004 (sec), leaf count = 55 \[ \text {DSolve}\left [a y''(x) \wp (x;\text {g2},\text {g3})+b y'(x) \wp '(x;\text {g2},\text {g3})+y(x) \left (c \left (6 \wp (x;\text {g2},\text {g3})^2-\frac {\text {g2}}{2}\right )+d\right )+y^{(4)}(x)=0,y(x),x\right ] \]

Maple: cpu = 0.561 (sec), leaf count = 60 \[ \left \{ y \left ( x \right ) ={\it DESol} \left ( \left \{ {\frac { {\rm d}^{4}}{{\rm d}{x}^{4}}}{\it \_Y} \left ( x \right ) +a{\it WeierstrassP} \left ( x,{\it g2},{\it g3} \right ) {\frac {{\rm d}^{2}}{ {\rm d}{x}^{2}}}{\it \_Y} \left ( x \right ) +b{\it WeierstrassPPrime} \left ( x,{\it g2},{\it g3} \right ) {\frac {\rm d}{{\rm d}x}}{\it \_Y} \left ( x \right ) + \left ( 6\,c \left ( {\it WeierstrassP} \left ( x,{ \it g2},{\it g3} \right ) \right ) ^{2}-{\frac {c{\it g2}}{2}}+d \right ) {\it \_Y} \left ( x \right ) \right \} , \left \{ {\it \_Y} \left ( x \right ) \right \} \right ) \right \} \]