2.1673   ODE No. 1673

\[ a \left (e^{y(x)}-1\right )+x^2 y''(x)=0 \] Mathematica : cpu = 22.8509 (sec), leaf count = 0


, could not solve

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

Maple : cpu = 0. (sec), leaf count = 0


, result contains DESol or ODESolStruc

\[y \relax (x ) = \textit {\_a} \boldsymbol {\mathrm {where}}\left [\left \{\frac {d}{d \textit {\_a}}\mathrm {\_}\mathrm {b}\left (\textit {\_a} \right )=\left (a \,{\mathrm e}^{\textit {\_a}}-a \right ) \textit {\_}b\left (\textit {\_a} \right )^{3}-\textit {\_}b\left (\textit {\_a} \right )^{2}\right \}, \left \{\textit {\_a} =y \relax (x ), \textit {\_}b\left (\textit {\_a} \right )=\frac {1}{x \left (\frac {d}{d x}y \relax (x )\right )}\right \}, \left \{x ={\mathrm e}^{\int \textit {\_}b\left (\textit {\_a} \right )d \textit {\_a} +c_{1}}, y \relax (x )=\textit {\_a} \right \}\right ]\]