\[ \boxed { {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) ={\frac {a \left ( {\frac {\rm d}{{\rm d}x}}f \left ( x \right ) \right ) {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) }{f \left ( x \right ) }}-{\frac {b \left ( f \left ( x \right ) \right ) ^{2\,a+1}y \left ( x \right ) }{f \left ( x \right ) }}=0} \]
Mathematica: cpu = 1.510692 (sec), leaf count = 36 \[ \text {DSolve}\left [y''(x)=-b y(x) f(x)^{2 a}-\frac {a f'(x) y'(x)}{f(x)},y(x),x\right ] \]
Maple: cpu = 0.016 (sec), leaf count = 37 \[ \left \{ y \left ( x \right ) ={\it \_C1}\,{{\rm e}^{\int \!i \left ( f \left ( x \right ) \right ) ^{a}\sqrt {b}\,{\rm d}x}}+{\it \_C2}\,{ {\rm e}^{-\int \!i \left ( f \left ( x \right ) \right ) ^{a}\sqrt {b} \,{\rm d}x}} \right \} \]