\[ f(x) (1-y(x)) y(x) y'(x)+2 (1-y(x)) y(x) y''(x)-\left ((1-2 y(x)) y'(x)^2\right )=0 \] ✓ Mathematica : cpu = 0.062119 (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 = 0.166 (sec), leaf count = 42
\[y \relax (x ) = \frac {\left (2 \,{\mathrm e}^{c_{1} \left (\int {\mathrm e}^{-\frac {\left (\int f \relax (x )d x \right )}{2}}d x \right )} c_{2}+1\right )^{2} {\mathrm e}^{\int -c_{1} {\mathrm e}^{\int -\frac {f \relax (x )}{2}d x}d x}}{8 c_{2}}\]