\[ y(x) y''(x)-a x^2=0 \] ✗ Mathematica : cpu = 24.2305 (sec), leaf count = 0 , could not solve
DSolve[-(a*x^2) + y[x]*Derivative[2][y][x] == 0, y[x], x]
✓ Maple : cpu = 0.544 (sec), leaf count = 100
\[ \left \{ y \left ( x \right ) ={\it ODESolStruc} \left ( {\it \_a}\, \left ( {{\rm e}^{\int \!{\it \_b} \left ( {\it \_a} \right ) \,{\rm d}{\it \_a}+{\it \_C1}}} \right ) ^{2},[ \left \{ {\frac {\rm d}{{\rm d}{\it \_a}}}{\it \_b} \left ( {\it \_a} \right ) ={\frac { \left ( 2\,{{\it \_a}}^{2}-a \right ) \left ( {\it \_b} \left ( {\it \_a} \right ) \right ) ^{3}}{{\it \_a}}}+3\, \left ( {\it \_b} \left ( {\it \_a} \right ) \right ) ^{2} \right \} , \left \{ {\it \_a}={\frac {y \left ( x \right ) }{{x}^{2}}},{\it \_b} \left ( {\it \_a} \right ) ={\frac {{x}^{2}}{x{\frac {\rm d}{{\rm d}x}}y \left ( x \right ) -2\,y \left ( x \right ) }} \right \} , \left \{ x={{\rm e}^{\int \!{\it \_b} \left ( {\it \_a} \right ) \,{\rm d}{\it \_a}+{\it \_C1}}},y \left ( x \right ) ={\it \_a}\, \left ( {{\rm e}^{\int \!{\it \_b} \left ( {\it \_a} \right ) \,{\rm d}{\it \_a}+{\it \_C1}}} \right ) ^{2} \right \} ] \right ) \right \} \]