\[ 2 f'(x) \left (y^{(3)}(x)-a^2 y'(x)\right )+f(x) \left (a^4 y(x)-2 a^2 y''(x)+y^{(4)}(x)\right )=0 \] ✗ Mathematica : cpu = 0.159509 (sec), leaf count = 0
DSolve[2*Derivative[1][f][x]*(-(a^2*Derivative[1][y][x]) + Derivative[3][y][x]) + f[x]*(a^4*y[x] - 2*a^2*Derivative[2][y][x] + Derivative[4][y][x]) == 0,y[x],x]
, could not solve
DSolve[2*Derivative[1][f][x]*(-(a^2*Derivative[1][y][x]) + Derivative[3][y][x]) + f[x]*(a^4*y[x] - 2*a^2*Derivative[2][y][x] + Derivative[4][y][x]) == 0, y[x], x]
✓ Maple : cpu = 0.02 (sec), leaf count = 67
dsolve(f*(diff(diff(diff(diff(y(x),x),x),x),x)-2*a^2*diff(diff(y(x),x),x)+a^4*y(x))+2*df*(diff(diff(diff(y(x),x),x),x)-a^2*diff(y(x),x))=0,y(x))
\[y \left (x \right ) = c_{1} {\mathrm e}^{-a x}+c_{2} {\mathrm e}^{a x}+c_{3} {\mathrm e}^{\frac {\left (-\mathit {df} +\sqrt {a^{2} f^{2}+\mathit {df}^{2}}\right ) x}{f}}+c_{4} {\mathrm e}^{-\frac {\left (\mathit {df} +\sqrt {a^{2} f^{2}+\mathit {df}^{2}}\right ) x}{f}}\]