\[ b y(x) f(x)^{2 a}-\frac {a f'(x) y'(x)}{f(x)}+y''(x)=0 \] ✓ Mathematica : cpu = 0.246015 (sec), leaf count = 135
\[\left \{\left \{y(x)\to \frac {1}{2} \left (e^{c_2+\int _1^x -i \sqrt {b} f(K[1])^a \, dK[1]}-2 c_1 \exp \left (-c_2-\int _1^x -i \sqrt {b} f(K[1])^a \, dK[1]\right )\right )\right \},\left \{y(x)\to \frac {1}{2} \left (e^{c_2+\int _1^x i \sqrt {b} f(K[2])^a \, dK[2]}-2 c_1 e^{-c_2-\int _1^x i \sqrt {b} f(K[2])^a \, dK[2]}\right )\right \}\right \}\]
✓ Maple : cpu = 0.018 (sec), leaf count = 37
\[ \left \{ y \left ( x \right ) ={\it \_C1}\,{{\rm e}^{\int \!i \left ( f \left ( x \right ) \right ) ^{a}\sqrt {b}\,{\rm d}x}}+{\it \_C2}\,{{\rm e}^{-\int \!i \left ( f \left ( x \right ) \right ) ^{a}\sqrt {b}\,{\rm d}x}} \right \} \]