\[ \boxed { \left ( {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) \right ) y \left ( x \right ) -a{x}^{2}=0} \]
Mathematica: cpu = 24.305086 (sec), leaf count = 20 \[ \text {DSolve}\left [y(x) y''(x)-a x^2=0,y(x),x\right ] \]
Maple: cpu = 1.856 (sec), leaf count = 102 \[ \left \{ y \left ( x \right ) ={\it ODESolStruc} \left ( {\it \_a}\, \left ( {{\rm e}^{\int \!{\it \_b} \left ( {\it \_a} \right ) \,{\rm d}{ \it \_a}+{\it \_C1}}} \right ) ^{2},[ \left \{ {\frac {\rm d}{{\rm d}{ \it \_a}}}{\it \_b} \left ( {\it \_a} \right ) ={\frac { \left ( 2\,{{ \it \_a}}^{2}-a \right ) \left ( {\it \_b} \left ( {\it \_a} \right ) \right ) ^{3}}{{\it \_a}}}+3\, \left ( {\it \_b} \left ( {\it \_a} \right ) \right ) ^{2} \right \} , \left \{ {\it \_a}={\frac {y \left ( x \right ) }{{x}^{2}}},{\it \_b} \left ( {\it \_a} \right ) =-{\frac {{x}^ {2}}{-x{\frac {\rm d}{{\rm d}x}}y \left ( x \right ) +2\,y \left ( x \right ) }} \right \} , \left \{ x={{\rm e}^{\int \!{\it \_b} \left ( { \it \_a} \right ) \,{\rm d}{\it \_a}+{\it \_C1}}},y \left ( x \right ) ={ \it \_a}\, \left ( {{\rm e}^{\int \!{\it \_b} \left ( {\it \_a} \right ) \,{\rm d}{\it \_a}+{\it \_C1}}} \right ) ^{2} \right \} ] \right ) \right \} \]