\[ y(x) \left (1-a^2 x^{2 n}\right )+y''(x)=0 \] ✗ Mathematica : cpu = 0.290983 (sec), leaf count = 0
DSolve[(1 - a^2*x^(2*n))*y[x] + Derivative[2][y][x] == 0,y[x],x]
, 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
dsolve(diff(diff(y(x),x),x)-(a^2*x^(2*n)-1)*y(x)=0,y(x))
, result contains DESol or ODESolStruc
\[y \left (x \right ) = \mathit {DESol}\left (\left \{\frac {d^{2}}{d x^{2}}\textit {\_Y} \left (x \right )+\left (-a^{2} x^{2 n}+1\right ) \textit {\_Y} \left (x \right )\right \}, \left \{\textit {\_Y} \left (x \right )\right \}\right )\]