\[ \boxed { 2\,y \left ( x \right ) \left ( 1-y \left ( x \right ) \right ) {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) - \left ( 1-2\,y \left ( x \right ) \right ) \left ( {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) \right ) ^{2}+y \left ( x \right ) \left ( 1-y \left ( x \right ) \right ) \left ( {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) \right ) f \left ( x \right ) =0} \]
Mathematica: cpu = 1.028631 (sec), leaf count = 95 \[ \left \{\left \{y(x)\to \frac {1}{4} \exp \left (-i \int _1^x c_1 \left (-e^{-\int _1^{K[3]} \frac {1}{2} f(K[1]) \, dK[1]}\right ) \, dK[3]-i c_2\right ) \left (1+\exp \left (i \int _1^x c_1 \left (-e^{-\int _1^{K[3]} \frac {1}{2} f(K[1]) \, dK[1]}\right ) \, dK[3]+i c_2\right )\right ){}^2\right \}\right \} \]
Maple: cpu = 0.094 (sec), leaf count = 59 \[ \left \{ y \left ( x \right ) ={\frac {1}{8\,{\it \_C2}} \left ( 4\, \left ( {{\rm e}^{{\it \_C1}\,\int \!{{\rm e}^{-1/2\,\int \!f \left ( x \right ) \,{\rm d}x}}\,{\rm d}x}} \right ) ^{2}{{\it \_C2}}^{2}+4\,{ {\rm e}^{{\it \_C1}\,\int \!{{\rm e}^{-1/2\,\int \!f \left ( x \right ) \,{\rm d}x}}\,{\rm d}x}}{\it \_C2}+1 \right ) \left ( {{\rm e}^{{\it \_C1}\,\int \!{{\rm e}^{-{\frac {\int \!f \left ( x \right ) \,{\rm d}x }{2}}}}\,{\rm d}x}} \right ) ^{-1}} \right \} \]