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 = 27.5652 (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 = 1.568 (sec), leaf count = 56

\[\left \{y \left (x \right ) = \mathit {ODESolStruc} \left (\textit {\_a} , \left [\left \{a \textit {\_}b\left (\textit {\_a} \right )+b \,{\mathrm e}^{\textit {\_a}}+\textit {\_}b\left (\textit {\_a} \right ) \left (\frac {d}{d \textit {\_a}}\mathrm {\_}\mathrm {b}\left (\textit {\_a} \right )\right )-2 a =0\right \}, \left \{\textit {\_a} =y \left (x \right ), \textit {\_}b\left (\textit {\_a} \right )=\frac {d}{d x}y \left (x \right )\right \}, \left \{x =c_{1}+\int \frac {1}{\textit {\_}b\left (\textit {\_a} \right )}d \textit {\_a} , y \left (x \right )=\textit {\_a} \right \}\right ]\right )\right \}\]