\[ a b (y(x)-1) y(x) y''(x)-\left (y'(x)^2 ((2 a b-a-b) y(x)+(1-a) b)\right )+f(x) (y(x)-1) y(x) y'(x)=0 \] ✓ Mathematica : cpu = 0.141123 (sec), leaf count = 69
DSolve[f[x]*(-1 + y[x])*y[x]*Derivative[1][y][x] - ((1 - a)*b + (-a - b + 2*a*b)*y[x])*Derivative[1][y][x]^2 + a*b*(-1 + y[x])*y[x]*Derivative[2][y][x] == 0,y[x],x]
\[\left \{\left \{y(x)\to \text {InverseFunction}\left [-a \text {$\#$1}^{\frac {1}{a}} \, _2F_1\left (\frac {1}{a},1-\frac {1}{b};1+\frac {1}{a};\text {$\#$1}\right )\& \right ]\left [\int _1^x\exp \left (-\int _1^{K[3]}\frac {f(K[1])}{a b}dK[1]\right ) c_1dK[3]+c_2\right ]\right \}\right \}\] ✓ Maple : cpu = 0.085 (sec), leaf count = 46
dsolve(a*b*y(x)*(-1+y(x))*diff(diff(y(x),x),x)-((2*a*b-a-b)*y(x)+(1-a)*b)*diff(y(x),x)^2+f*y(x)*(-1+y(x))*diff(y(x),x)=0,y(x))
\[c_{1} {\mathrm e}^{-\frac {f x}{b a}}-c_{2}+\int _{}^{y \left (x \right )}\frac {\textit {\_a}^{\frac {1}{a}} \left (\textit {\_a} -1\right )^{\frac {1}{b}}}{\textit {\_a} \left (\textit {\_a} -1\right )}d \textit {\_a} = 0\]