\[ b y(x) f(x)^{2 a}-\frac {a f'(x) y'(x)}{f(x)}+y''(x)=0 \] ✓ Mathematica : cpu = 0.26827 (sec), leaf count = 299
\[\left \{\left \{y(x)\to -\frac {\sqrt {c_1} \exp \left (-c_2-\int _1^x -i \sqrt {b} f(K[1])^a \, dK[1]\right ) \left (-1+\exp \left (2 \left (c_2+\int _1^x -i \sqrt {b} f(K[1])^a \, dK[1]\right )\right )\right )}{\sqrt {2}}\right \},\left \{y(x)\to \frac {\sqrt {c_1} \exp \left (-c_2-\int _1^x -i \sqrt {b} f(K[1])^a \, dK[1]\right ) \left (-1+\exp \left (2 \left (c_2+\int _1^x -i \sqrt {b} f(K[1])^a \, dK[1]\right )\right )\right )}{\sqrt {2}}\right \},\left \{y(x)\to -\frac {\sqrt {c_1} e^{-c_2-\int _1^x i \sqrt {b} f(K[2])^a \, dK[2]} \left (-1+\exp \left (2 \left (c_2+\int _1^x i \sqrt {b} f(K[2])^a \, dK[2]\right )\right )\right )}{\sqrt {2}}\right \},\left \{y(x)\to \frac {\sqrt {c_1} e^{-c_2-\int _1^x i \sqrt {b} f(K[2])^a \, dK[2]} \left (-1+\exp \left (2 \left (c_2+\int _1^x i \sqrt {b} f(K[2])^a \, dK[2]\right )\right )\right )}{\sqrt {2}}\right \}\right \}\]
✓ Maple : cpu = 0.03 (sec), leaf count = 37
\[ \left \{ y \left ( x \right ) ={\it \_C1}\,{{\rm e}^{\int \!i \left ( f \left ( x \right ) \right ) ^{a}\sqrt {b}\,{\rm d}x}}+{\it \_C2}\,{{\rm e}^{-\int \!i \left ( f \left ( x \right ) \right ) ^{a}\sqrt {b}\,{\rm d}x}} \right \} \]