2.1665   ODE No. 1665

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

\[ 2 y'(x)+x y''(x)+x e^{y(x)}=0 \] Mathematica : cpu = 0.0929852 (sec), leaf count = 0 , could not solve

DSolve[E^y[x]*x + 2*Derivative[1][y][x] + x*Derivative[2][y][x] == 0, y[x], x]

Maple : cpu = 0.624 (sec), leaf count = 84

\[ \left \{ y \left ( x \right ) ={\it ODESolStruc} \left ( {\it \_a}-2\,\int \!{\it \_b} \left ( {\it \_a} \right ) \,{\rm d}{\it \_a}-2\,{\it \_C1},[ \left \{ {\frac {\rm d}{{\rm d}{\it \_a}}}{\it \_b} \left ( {\it \_a} \right ) = \left ( {{\rm e}^{{\it \_a}}}-2 \right ) \left ( {\it \_b} \left ( {\it \_a} \right ) \right ) ^{3}+ \left ( {\it \_b} \left ( {\it \_a} \right ) \right ) ^{2} \right \} , \left \{ {\it \_a}=y \left ( x \right ) +2\,\ln \left ( x \right ) ,{\it \_b} \left ( {\it \_a} \right ) = \left ( x{\frac {\rm d}{{\rm d}x}}y \left ( x \right ) +2 \right ) ^{-1} \right \} , \left \{ x={{\rm e}^{\int \!{\it \_b} \left ( {\it \_a} \right ) \,{\rm d}{\it \_a}+{\it \_C1}}},y \left ( x \right ) ={\it \_a}-2\,\int \!{\it \_b} \left ( {\it \_a} \right ) \,{\rm d}{\it \_a}-2\,{\it \_C1} \right \} ] \right ) \right \} \]