\[ -(a-1) (2 y(x)-1) y'(x)^2+a (y(x)-1) y(x) y''(x)+f(x) (y(x)-1) y(x) y'(x)=0 \] ✓ Mathematica : cpu = 0.122435 (sec), leaf count = 83
\[\left \{\left \{y(x)\to \text {InverseFunction}\left [a \text {$\#$1}^{-1/a} (-(\text {$\#$1}-1) \text {$\#$1})^{\frac {1}{a}} \, _2F_1\left (\frac {1}{a},\frac {a-1}{a};1+\frac {1}{a};1-\text {$\#$1}\right )\& \right ]\left [\int _1^x\exp \left (-\int _1^{K[3]}\frac {f(K[1])}{a}dK[1]\right ) c_1dK[3]+c_2\right ]\right \}\right \}\] ✓ Maple : cpu = 0.272 (sec), leaf count = 40
\[ \left \{ {\it \_C1}\,{{\rm e}^{-{\frac {fx}{a}}}}-{\it \_C2}+\int ^{y \left ( x \right ) }\!{\frac {\sqrt [a]{{\it \_a}\, \left ( {\it \_a}-1 \right ) }}{{\it \_a}\, \left ( {\it \_a}-1 \right ) }}{d{\it \_a}}=0 \right \} \]