\[ x^2 y''(x)-a \left (y(x)^n-y(x)\right )=0 \] ✗ Mathematica : cpu = 9.74427 (sec), leaf count = 0
DSolve[-(a*(-y[x] + y[x]^n)) + x^2*Derivative[2][y][x] == 0,y[x],x]
, could not solve
DSolve[-(a*(-y[x] + y[x]^n)) + x^2*Derivative[2][y][x] == 0, y[x], x]
✗ Maple : cpu = 0. (sec), leaf count = 0
dsolve(x^2*diff(diff(y(x),x),x)-a*(y(x)^n-y(x))=0,y(x))
, result contains DESol or ODESolStruc
\[y \left (x \right ) = \textit {\_a} \boldsymbol {\mathrm {where}}\left [\left \{\frac {d}{d \textit {\_a}}\mathrm {\_}\mathrm {b}\left (\textit {\_a} \right )=\left (-\textit {\_a}^{n} a +a \textit {\_a} \right ) \textit {\_}b\left (\textit {\_a} \right )^{3}-\textit {\_}b\left (\textit {\_a} \right )^{2}\right \}, \left \{\textit {\_a} =y \left (x \right ), \textit {\_}b\left (\textit {\_a} \right )=\frac {1}{x \left (\frac {d}{d x}y \left (x \right )\right )}\right \}, \left \{x ={\mathrm e}^{\int \textit {\_}b\left (\textit {\_a} \right )d \textit {\_a} +c_{1}}, y \left (x \right )=\textit {\_a} \right \}\right ]\]