\[ a \left (e^{y(x)}-1\right )+x^2 y''(x)=0 \] ✗ Mathematica : cpu = 26.4981 (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 = 0.797 (sec), leaf count = 60
\[\left \{y \left (x \right ) = \mathit {ODESolStruc} \left (\textit {\_a} , \left [\left \{\frac {d}{d \textit {\_a}}\mathrm {\_}\mathrm {b}\left (\textit {\_a} \right )=\left (\left ({\mathrm e}^{\textit {\_a}}-1\right ) a \textit {\_}b\left (\textit {\_a} \right )-1\right ) \textit {\_}b\left (\textit {\_a} \right )^{2}\right \}, \left \{\textit {\_a} =y \left (x \right ), \textit {\_}b\left (\textit {\_a} \right )=\frac {1}{x \left (\frac {d}{d x}y \left (x \right )\right )}\right \}, \left \{x ={\mathrm e}^{c_{1}+\int \textit {\_}b\left (\textit {\_a} \right )d \textit {\_a}}, y \left (x \right )=\textit {\_a} \right \}\right ]\right )\right \}\]