2.1618   ODE No. 1618

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

\[ a y'(x)-2 a+b e^{y(x)}+y''(x)=0 \] Mathematica : cpu = 26.4642 (sec), leaf count = 0 , could not solve

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

Maple : cpu = 0.915 (sec), leaf count = 56

\[ \left \{ y \left ( x \right ) ={\it ODESolStruc} \left ( {\it \_a},[ \left \{ \left ( {\frac {\rm d}{{\rm d}{\it \_a}}}{\it \_b} \left ( {\it \_a} \right ) \right ) {\it \_b} \left ( {\it \_a} \right ) +a{\it \_b} \left ( {\it \_a} \right ) +b{{\rm e}^{{\it \_a}}}-2\,a=0 \right \} , \left \{ {\it \_a}=y \left ( x \right ) ,{\it \_b} \left ( {\it \_a} \right ) ={\frac {\rm d}{{\rm d}x}}y \left ( x \right ) \right \} , \left \{ x=\int \! \left ( {\it \_b} \left ( {\it \_a} \right ) \right ) ^{-1}\,{\rm d}{\it \_a}+{\it \_C1},y \left ( x \right ) ={\it \_a} \right \} ] \right ) \right \} \]