\[ a \left (e^{y(x)}-1\right )+x^2 y''(x)=0 \] ✗ Mathematica : cpu = 25.3515 (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 = 0.859 (sec), leaf count = 60
\[ \left \{ y \left ( x \right ) ={\it ODESolStruc} \left ( {\it \_a},[ \left \{ {\frac {\rm d}{{\rm d}{\it \_a}}}{\it \_b} \left ( {\it \_a} \right ) = \left ( {\it \_b} \left ( {\it \_a} \right ) \right ) ^{2} \left ( -1+a \left ( {{\rm e}^{{\it \_a}}}-1 \right ) {\it \_b} \left ( {\it \_a} \right ) \right ) \right \} , \left \{ {\it \_a}=y \left ( x \right ) ,{\it \_b} \left ( {\it \_a} \right ) ={\frac {1}{x{\frac {\rm d}{{\rm d}x}}y \left ( x \right ) }} \right \} , \left \{ x={{\rm e}^{\int \!{\it \_b} \left ( {\it \_a} \right ) \,{\rm d}{\it \_a}+{\it \_C1}}},y \left ( x \right ) ={\it \_a} \right \} ] \right ) \right \} \]