\[ y''(x)=-b y(x) f(x)^{2 a}-\frac {a f'(x) y'(x)}{f(x)} \] ✗ Mathematica : cpu = 1.10424 (sec), leaf count = 0 , 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 = 0.038 (sec), leaf count = 37
\[ \left \{ y \left ( x \right ) ={\it \_C1}\,{{\rm e}^{\int \!i \left ( f \left ( x \right ) \right ) ^{a}\sqrt {b}\,{\rm d}x}}+{\it \_C2}\,{{\rm e}^{-\int \!i \left ( f \left ( x \right ) \right ) ^{a}\sqrt {b}\,{\rm d}x}} \right \} \]