8.76   ODE No. 1666

\[ \boxed { x{\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) +a{\frac {\rm d}{{\rm d}x}}y \left ( x \right ) +bx{{\rm e}^{y \left ( x \right ) }}=0} \]

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

Mathematica: cpu = 0.593575 (sec), leaf count = 26 \[ \text {DSolve}\left [a y'(x)+b x e^{y(x)}+x y''(x)=0,y(x),x\right ] \]

Maple: cpu = 0.608 (sec), leaf count = 93 \[ \left \{ y \left ( x \right ) ={\it ODESolStruc} \left ( {\it \_a}-2\, \int \!{\it \_b} \left ( {\it \_a} \right ) \,{\rm d}{\it \_a}-2\,{\it \_C1},[ \left \{ {\frac {\rm d}{{\rm d}{\it \_a}}}{\it \_b} \left ( { \it \_a} \right ) = \left ( b{{\rm e}^{{\it \_a}}}-2\,a+2 \right ) \left ( {\it \_b} \left ( {\it \_a} \right ) \right ) ^{3}+ \left ( a-1 \right ) \left ( {\it \_b} \left ( {\it \_a} \right ) \right ) ^{2} \right \} , \left \{ {\it \_a}=y \left ( x \right ) +2\,\ln \left ( x \right ) ,{\it \_b} \left ( {\it \_a} \right ) = \left ( x{\frac {\rm d}{ {\rm d}x}}y \left ( x \right ) +2 \right ) ^{-1} \right \} , \left \{ x={ {\rm e}^{\int \!{\it \_b} \left ( {\it \_a} \right ) \,{\rm d}{\it \_a}+ {\it \_C1}}},y \left ( x \right ) ={\it \_a}-2\,\int \!{\it \_b} \left ( {\it \_a} \right ) \,{\rm d}{\it \_a}-2\,{\it \_C1} \right \} ] \right ) \right \} \]