\[ y''(x)=-b y(x) f(x)^{2 a}-\frac {a f'(x) y'(x)}{f(x)} \] ✗ Mathematica : cpu = 1.08347 (sec), leaf count = 0
DSolve[Derivative[2][y][x] == -(b*f[x]^(2*a)*y[x]) - (a*Derivative[1][f][x]*Derivative[1][y][x])/f[x],y[x],x]
, could not solve
DSolve[Derivative[2][y][x] == -(b*f[x]^(2*a)*y[x]) - (a*Derivative[1][f][x]*Derivative[1][y][x])/f[x], y[x], x]
✓ Maple : cpu = 0.02 (sec), leaf count = 37
dsolve(diff(diff(y(x),x),x) = a*diff(f(x),x)/f(x)*diff(y(x),x)-b*f(x)^(2*a+1)/f(x)*y(x),y(x))
\[y \left (x \right ) = c_{1} {\mathrm e}^{\int i f \left (x \right )^{a} \sqrt {b}d x}+c_{2} {\mathrm e}^{-\left (\int i f \left (x \right )^{a} \sqrt {b}d x \right )}\]