\[ a^2 y(x)^n+x^4 y''(x)=0 \] ✗ Mathematica : cpu = 0.0332063 (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 = 1.063 (sec), leaf count = 160
\[ \left \{ y \left ( x \right ) ={\it ODESolStruc} \left ( {\it \_a}\,{{\rm e}^{\int \!{\it \_b} \left ( {\it \_a} \right ) \,{\rm d}{\it \_a}+{\it \_C1}}},[ \left \{ {\frac {\rm d}{{\rm d}{\it \_a}}}{\it \_b} \left ( {\it \_a} \right ) = \left ( {\frac {{n}^{2}{{\it \_a}}^{n}{a}^{2}}{4}}-{\frac {n{{\it \_a}}^{n}{a}^{2}}{2}}+{\frac {{{\it \_a}}^{n}{a}^{2}}{4}}-{\frac {{\it \_a}\,n}{2}}+{\frac {3\,{\it \_a}}{2}} \right ) \left ( {\it \_b} \left ( {\it \_a} \right ) \right ) ^{3}+ \left ( -{\frac {n}{2}}+{\frac {5}{2}} \right ) \left ( {\it \_b} \left ( {\it \_a} \right ) \right ) ^{2} \right \} , \left \{ {\it \_a}=y \left ( x \right ) {x}^{-2\, \left ( n-1 \right ) ^{-1}},{\it \_b} \left ( {\it \_a} \right ) =-2\,{\frac {1}{-nx{\frac {\rm d}{{\rm d}x}}y \left ( x \right ) +x{\frac {\rm d}{{\rm d}x}}y \left ( x \right ) +2\,y \left ( x \right ) } \left ( {x}^{-2\, \left ( n-1 \right ) ^{-1}} \right ) ^{-1}} \right \} , \left \{ x={{\rm e}^{{\frac { \left ( \int \!{\it \_b} \left ( {\it \_a} \right ) \,{\rm d}{\it \_a}+{\it \_C1} \right ) n}{2}}-{\frac {\int \!{\it \_b} \left ( {\it \_a} \right ) \,{\rm d}{\it \_a}}{2}}-{\frac {{\it \_C1}}{2}}}},y \left ( x \right ) ={\it \_a}\,{{\rm e}^{\int \!{\it \_b} \left ( {\it \_a} \right ) \,{\rm d}{\it \_a}+{\it \_C1}}} \right \} ] \right ) \right \} \]