8.225   ODE No. 1815

\[ \boxed { h \left ( y \left ( x \right ) \right ) {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) -\mbox {D} \left ( h \right ) \left ( y \left ( x \right ) \right ) \left ( {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) \right ) ^{2}- \left ( h \left ( y \left ( x \right ) \right ) \right ) ^{2}j \left ( x,{\frac {{\frac {\rm d}{{\rm d}x}}y \left ( x \right ) }{h \left ( y \left ( x \right ) \right ) }} \right ) =0} \]

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

Mathematica: cpu = 1.169649 (sec), leaf count = 45 \[ \text {DSolve}\left [h(y(x))^2 \left (-j\left (x,\frac {y'(x)}{h(y(x))}\right )\right )+h(y(x)) y''(x)-h(y(x)) y'(x)^2=0,y(x),x\right ] \]

Maple: cpu = 0.780 (sec), leaf count = 74 \[ \left \{ y \left ( x \right ) ={\it ODESolStruc} \left ( {\it RootOf} \left ( \int \!{\it \_b} \left ( {\it \_a} \right ) \,{\rm d}{\it \_a}+{ \it \_C1}-\int ^{{\it \_Z}}\! \left ( h \left ( {\it \_f} \right ) \right ) ^{-1}{d{\it \_f}} \right ) ,[ \left \{ {\frac {\rm d}{{\rm d}{ \it \_a}}}{\it \_b} \left ( {\it \_a} \right ) =j \left ( {\it \_a},{\it \_b} \left ( {\it \_a} \right ) \right ) \right \} , \left \{ {\it \_a}=x ,{\it \_b} \left ( {\it \_a} \right ) ={\frac {{\frac {\rm d}{{\rm d}x}} y \left ( x \right ) }{h \left ( y \left ( x \right ) \right ) }} \right \} , \left \{ x={\it \_a},y \left ( x \right ) ={\it RootOf} \left ( \int \!{ \it \_b} \left ( {\it \_a} \right ) \,{\rm d}{\it \_a}+{\it \_C1}-\int ^ {{\it \_Z}}\! \left ( h \left ( {\it \_f} \right ) \right ) ^{-1}{d{\it \_f}} \right ) \right \} ] \right ) \right \} \]