\[ a^2 y(x)^n+x^4 y''(x)=0 \] ✗ Mathematica : cpu = 0.0222477 (sec), leaf count = 0 , could not solve
DSolve[a^2*y[x]^n + x^4*Derivative[2][y][x] == 0, y[x], x]
✓ Maple : cpu = 1.418 (sec), leaf count = 128
\[ \left \{ y \left ( x \right ) ={\it ODESolStruc} \left ( {\it \_a}\,{{\rm e}^{\int \!{\it \_b} \left ( {\it \_a} \right ) \,{\rm d}{\it \_a}+{\it \_C1}}},[ \left \{ {\frac {\rm d}{{\rm d}{\it \_a}}}{\it \_b} \left ( {\it \_a} \right ) ={\frac { \left ( {a}^{2}{\it \_b} \left ( {\it \_a} \right ) \left ( n-1 \right ) ^{2}{{\it \_a}}^{n}-2\,{\it \_a}\, \left ( n-3 \right ) {\it \_b} \left ( {\it \_a} \right ) -2\,n+10 \right ) \left ( {\it \_b} \left ( {\it \_a} \right ) \right ) ^{2}}{4}} \right \} , \left \{ {\it \_a}=y \left ( x \right ) {x}^{-2\, \left ( n-1 \right ) ^{-1}},{\it \_b} \left ( {\it \_a} \right ) =2\,{\frac {1}{ \left ( n-1 \right ) x{\frac {\rm d}{{\rm d}x}}y \left ( x \right ) -2\,y \left ( x \right ) } \left ( {x}^{-2\, \left ( n-1 \right ) ^{-1}} \right ) ^{-1}} \right \} , \left \{ x={{\rm e}^{{\frac { \left ( \int \!{\it \_b} \left ( {\it \_a} \right ) \,{\rm d}{\it \_a}+{\it \_C1} \right ) \left ( n-1 \right ) }{2}}}},y \left ( x \right ) ={\it \_a}\,{{\rm e}^{\int \!{\it \_b} \left ( {\it \_a} \right ) \,{\rm d}{\it \_a}+{\it \_C1}}} \right \} ] \right ) \right \} \]