\[ f(x) (1-y(x)) y(x) y'(x)+2 (1-y(x)) y(x) y''(x)-\left ((1-2 y(x)) y'(x)^2\right )=0 \] ✓ Mathematica : cpu = 0.062119 (sec), leaf count = 53
DSolve[f[x]*(1 - y[x])*y[x]*Derivative[1][y][x] - (1 - 2*y[x])*Derivative[1][y][x]^2 + 2*(1 - y[x])*y[x]*Derivative[2][y][x] == 0,y[x],x]
\[\left \{\left \{y(x)\to 1-\sin ^2\left (\frac {1}{2} \left (-\int _1^x-\exp \left (-\int _1^{K[3]}\frac {1}{2} f(K[1])dK[1]\right ) c_1dK[3]-c_2\right )\right )\right \}\right \}\] ✓ Maple : cpu = 0.166 (sec), leaf count = 42
dsolve(2*y(x)*(1-y(x))*diff(diff(y(x),x),x)-(1-2*y(x))*diff(y(x),x)^2+y(x)*(1-y(x))*diff(y(x),x)*f(x)=0,y(x))
\[y \left (x \right ) = \frac {\left (2 \,{\mathrm e}^{c_{1} \left (\int {\mathrm e}^{-\frac {\left (\int f \left (x \right )d x \right )}{2}}d x \right )} c_{2}+1\right )^{2} {\mathrm e}^{\int -c_{1} {\mathrm e}^{\int -\frac {f \left (x \right )}{2}d x}d x}}{8 c_{2}}\]