\[ y'(x)^n-f(x)^n (y(x)-a)^{n+1} (y(x)-b)^{n-1}=0 \] ✓ Mathematica : cpu = 0.44487 (sec), leaf count = 84
\[\left \{\left \{y(x)\to \frac {-a (a-b)^n \left (\int _1^x (-1)^{\frac {1}{n}+1} f(K[1]) \, dK[1]+c_1\right ){}^n-b n^n}{-(a-b)^n \left (\int _1^x (-1)^{\frac {1}{n}+1} f(K[1]) \, dK[1]+c_1\right ){}^n-n^n}\right \}\right \}\] ✓ Maple : cpu = 0.455 (sec), leaf count = 55
\[ \left \{ y \left ( x \right ) ={1 \left ( b \left ( -{\frac {n}{ \left ( a-b \right ) \left ( \int \!f \left ( x \right ) \,{\rm d}x+{\it \_C1} \right ) }} \right ) ^{n}-a \right ) \left ( -1+ \left ( -{\frac {n}{ \left ( a-b \right ) \left ( \int \!f \left ( x \right ) \,{\rm d}x+{\it \_C1} \right ) }} \right ) ^{n} \right ) ^{-1}} \right \} \]