2.1666   ODE No. 1666

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

\[ a y'(x)+b x e^{y(x)}+x y''(x)=0 \] Mathematica : cpu = 0.240117 (sec), leaf count = 0 , could not solve

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

Maple : cpu = 1.125 (sec), leaf count = 93

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