\[ \boxed { {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) -{\frac {a \left ( {\frac {\rm d}{{\rm d}x}}f \left ( x \right ) \right ) {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) }{f \left ( x \right ) }}+b \left ( f \left ( x \right ) \right ) ^{2\,a}y \left ( x \right ) =0} \]
Mathematica: cpu = 0.237530 (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 = 0.016 (sec), leaf count = 37 \[ \left \{ y \left ( x \right ) ={\it \_C1}\,{{\rm e}^{\int \!i \left ( f \left ( x \right ) \right ) ^{a}\sqrt {b}\,{\rm d}x}}+{\it \_C2}\,{ {\rm e}^{-\int \!i \left ( f \left ( x \right ) \right ) ^{a}\sqrt {b} \,{\rm d}x}} \right \} \]