\[ -y(x) f'(x)+2 f(x) y'(x)+2 f(x) y(x)^2-2 f(x)^2=0 \] ✓ Mathematica : cpu = 0.148826 (sec), leaf count = 39
\[\left \{\left \{y(x)\to i \sqrt {f(x)} \tan \left (i \int _1^x-\sqrt {f(K[1])}dK[1]+c_1\right )\right \}\right \}\] ✓ Maple : cpu = 0.049 (sec), leaf count = 23
\[y \relax (x ) = i \tan \left (-i \left (\int \sqrt {f \relax (x )}d x \right )+c_{1}\right ) \sqrt {f \relax (x )}\]