\[ f(x) (1-y(x)) y(x) y'(x)-(1-2 y(x)) y'(x)^2+2 (1-y(x)) y(x) y''(x)=0 \] ✓ Mathematica : cpu = 0.0596991 (sec), leaf count = 53
\[\left \{\left \{y(x)\to 1-\sin ^2\left (\frac {1}{2} \left (-\int _1^x-\exp \left (-\int _1^{K[3]}\frac {1}{2} f(K[1])dK[1]\right ) c_1dK[3]-c_2\right )\right )\right \}\right \}\] ✓ Maple : cpu = 1.088 (sec), leaf count = 42
\[ \left \{ y \left ( x \right ) ={\frac {1}{8\,{\it \_C2}} \left ( 2\,{{\rm e}^{{\it \_C1}\,\int \!{{\rm e}^{-1/2\,\int \!f \left ( x \right ) \,{\rm d}x}}\,{\rm d}x}}{\it \_C2}+1 \right ) ^{2} \left ( {{\rm e}^{{\it \_C1}\,\int \!{{\rm e}^{-{\frac {\int \!f \left ( x \right ) \,{\rm d}x}{2}}}}\,{\rm d}x}} \right ) ^{-1}} \right \} \]