ODE No. 201

\[ -y(x) f'(x)+2 f(x) y'(x)+2 f(x) y(x)^2-2 f(x)^2=0 \]

✓ Mathematica : cpu = 0.104167 (sec), leaf count = 39

DSolve[-2*f[x]^2 + 2*f[x]*y[x]^2 - y[x]*Derivative[1][f][x] + 2*f[x]*Derivative[1][y][x] == 0,y[x],x]

\[\left \{\left \{y(x)\to i \sqrt {f(x)} \tan \left (i \int _1^x-\sqrt {f(K[1])}dK[1]+c_1\right )\right \}\right \}\]

✓ Maple : cpu = 0.059 (sec), leaf count = 23

dsolve(2*f(x)*diff(y(x),x)+2*f(x)*y(x)^2-diff(f(x),x)*y(x)-2*f(x)^2 = 0,y(x))

\[y \left (x \right ) = i \tan \left (-i \left (\int \sqrt {f \left (x \right )}d x \right )+c_{1} \right ) \sqrt {f \left (x \right )}\]