\[ a (y(x)-1) y(x) y''(x)-(a-1) (2 y(x)-1) y'(x)^2+f(x) (y(x)-1) y(x) y'(x)=0 \] ✓ Mathematica : cpu = 1.32788 (sec), leaf count = 113
\[\left \{\left \{y(x)\to \text {InverseFunction}\left [-\frac {a (1-\text {$\#$1})^{-1/a} (-(\text {$\#$1}-1) \text {$\#$1})^{\frac {1}{a}} \left ((a+1) \, _2F_1\left (-\frac {1}{a},\frac {1}{a};1+\frac {1}{a};\text {$\#$1}\right )+\text {$\#$1} \, _2F_1\left (1+\frac {1}{a},\frac {a-1}{a};2+\frac {1}{a};\text {$\#$1}\right )\right )}{a+1}\& \right ]\left [\int _1^x c_1 e^{-\int _1^{K[3]} \frac {f(K[1])}{a} \, dK[1]} \, dK[3]+c_2\right ]\right \}\right \}\] ✓ Maple : cpu = 0.076 (sec), leaf count = 40
\[ \left \{ {\it \_C1}\,{{\rm e}^{-{\frac {fx}{a}}}}-{\it \_C2}+\int ^{y \left ( x \right ) }\!{\frac {\sqrt [a]{{\it \_a}\, \left ( {\it \_a}-1 \right ) }}{{\it \_a}\, \left ( {\it \_a}-1 \right ) }}{d{\it \_a}}=0 \right \} \]