\[ x^2 y''(x)-a \left (y(x)^n-y(x)\right )=0 \] ✗ Mathematica : cpu = 17.4745 (sec), leaf count = 0 , could not solve
DSolve[-(a*(-y[x] + y[x]^n)) + x^2*Derivative[2][y][x] == 0, y[x], x]
✓ Maple : cpu = 1.101 (sec), leaf count = 67
\[ \left \{ y \left ( x \right ) ={\it ODESolStruc} \left ( {\it \_a},[ \left \{ {\frac {\rm d}{{\rm d}{\it \_a}}}{\it \_b} \left ( {\it \_a} \right ) = \left ( -{{\it \_a}}^{n}a+a{\it \_a} \right ) \left ( {\it \_b} \left ( {\it \_a} \right ) \right ) ^{3}- \left ( {\it \_b} \left ( {\it \_a} \right ) \right ) ^{2} \right \} , \left \{ {\it \_a}=y \left ( x \right ) ,{\it \_b} \left ( {\it \_a} \right ) ={\frac {1}{x{\frac {\rm d}{{\rm d}x}}y \left ( x \right ) }} \right \} , \left \{ x={{\rm e}^{\int \!{\it \_b} \left ( {\it \_a} \right ) \,{\rm d}{\it \_a}+{\it \_C1}}},y \left ( x \right ) ={\it \_a} \right \} ] \right ) \right \} \]