\[ y'(x)^n-f(x)^n (y(x)-a)^{n+1} (y(x)-b)^{n-1}=0 \] ✓ Mathematica : cpu = 0.166825 (sec), leaf count = 86
DSolve[-(f[x]^n*(-a + y[x])^(1 + n)*(-b + y[x])^(-1 + n)) + Derivative[1][y][x]^n == 0,y[x],x]
\[\left \{\left \{y(x)\to \frac {-b n^n-a (a-b)^n \left (\int _1^x(-1)^{1+\frac {1}{n}} f(K[1])dK[1]+c_1\right ){}^n}{-n^n-(a-b)^n \left (\int _1^x(-1)^{1+\frac {1}{n}} f(K[1])dK[1]+c_1\right ){}^n}\right \}\right \}\] ✓ Maple : cpu = 0.67 (sec), leaf count = 55
dsolve(diff(y(x),x)^n-f(x)^n*(y(x)-a)^(n+1)*(y(x)-b)^(n-1)=0,y(x))
\[y \left (x \right ) = \frac {\left (-\frac {n}{\left (a -b \right ) \left (\int f \left (x \right )d x +c_{1}\right )}\right )^{n} b -a}{-1+\left (-\frac {n}{\left (a -b \right ) \left (\int f \left (x \right )d x +c_{1}\right )}\right )^{n}}\]