8.54   ODE No. 1644

\[ \boxed { {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) +h \left ( y \left ( x \right ) \right ) \left ( {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) \right ) ^{2}+j \left ( y \left ( x \right ) \right ) {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) +k \left ( y \left ( x \right ) \right ) =0} \]

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

Mathematica: cpu = 62.318914 (sec), leaf count = 32 \[ \text {DSolve}\left [h(y(x)) y'(x)^2+j(y(x)) y'(x)+k(y(x))+y''(x)=0,y(x),x\right ] \]

Maple: cpu = 0.374 (sec), leaf count = 59 \[ \left \{ y \left ( x \right ) ={\it ODESolStruc} \left ( {\it \_a},[ \left \{ \left ( {\frac {\rm d}{{\rm d}{\it \_a}}}{\it \_b} \left ( { \it \_a} \right ) \right ) {\it \_b} \left ( {\it \_a} \right ) +h \left ( {\it \_a} \right ) \left ( {\it \_b} \left ( {\it \_a} \right ) \right ) ^{2}+j \left ( {\it \_a} \right ) {\it \_b} \left ( {\it \_a} \right ) +k \left ( {\it \_a} \right ) =0 \right \} , \left \{ {\it \_a}=y \left ( x \right ) ,{\it \_b} \left ( {\it \_a} \right ) ={\frac {\rm d}{ {\rm d}x}}y \left ( x \right ) \right \} , \left \{ x=\int \! \left ( { \it \_b} \left ( {\it \_a} \right ) \right ) ^{-1}\,{\rm d}{\it \_a}+{ \it \_C1},y \left ( x \right ) ={\it \_a} \right \} ] \right ) \right \} \]