\[ x^2 y''(x)-a \left (y(x)^n-y(x)\right )=0 \] ✗ Mathematica : cpu = 12.8657 (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 = 1.155 (sec), leaf count = 65
\[\left \{y \left (x \right ) = \mathit {ODESolStruc} \left (\textit {\_a} , \left [\left \{\frac {d}{d \textit {\_a}}\mathrm {\_}\mathrm {b}\left (\textit {\_a} \right )=\left (\textit {\_a} a \textit {\_}b\left (\textit {\_a} \right )-a \,\textit {\_a}^{n} \textit {\_}b\left (\textit {\_a} \right )-1\right ) \textit {\_}b\left (\textit {\_a} \right )^{2}\right \}, \left \{\textit {\_a} =y \left (x \right ), \textit {\_}b\left (\textit {\_a} \right )=\frac {1}{x \left (\frac {d}{d x}y \left (x \right )\right )}\right \}, \left \{x ={\mathrm e}^{c_{1}+\int \textit {\_}b\left (\textit {\_a} \right )d \textit {\_a}}, y \left (x \right )=\textit {\_a} \right \}\right ]\right )\right \}\]