\[ y'(x)^n-f(x)^n (y(x)-a)^{n+1} (y(x)-b)^{n-1}=0 \] ✓ Mathematica : cpu = 0.409113 (sec), leaf count = 79
\[\left \{\left \{y(x)\to \frac {a (a-b)^n \left (\int _1^x (-1)^{\frac {1}{n}+1} f(K[1]) \, dK[1]+c_1\right ){}^n+b n^n}{(a-b)^n \left (\int _1^x (-1)^{\frac {1}{n}+1} f(K[1]) \, dK[1]+c_1\right ){}^n+n^n}\right \}\right \}\]
✓ Maple : cpu = 0.893 (sec), leaf count = 55
\[ \left \{ y \left ( x \right ) ={1 \left ( \left ( -{\frac {n}{ \left ( a-b \right ) \left ( \int \!f \left ( x \right ) \,{\rm d}x+{\it \_C1} \right ) }} \right ) ^{n}b-a \right ) \left ( -1+ \left ( -{\frac {n}{ \left ( a-b \right ) \left ( \int \!f \left ( x \right ) \,{\rm d}x+{\it \_C1} \right ) }} \right ) ^{n} \right ) ^{-1}} \right \} \]