\[ y(x) \left (1-a^2 x^{2 n}\right )+y''(x)=0 \] ✗ Mathematica : cpu = 0.332561 (sec), leaf count = 0 , could not solve
DSolve[(1 - a^2*x^(2*n))*y[x] + Derivative[2][y][x] == 0, y[x], x]
✗ Maple : cpu = 0. (sec), leaf count = 0 , result contains DESol
\[\{y \left (x \right ) = \mathit {DESol}\left (\left \{\left (-a^{2} x^{2 n}+1\right ) \textit {\_Y} \left (x \right )+\frac {d^{2}}{d x^{2}}\textit {\_Y} \left (x \right )\right \}, \left \{\textit {\_Y} \left (x \right )\right \}\right )\}\]