4 y(x)^2 (1-y(x)) \left(-f'(x)+f(x)^2-g'(x)-g(x)^2\right)-4 y(x) y'(x) (f(x) y(x)+g(x))+(1-y(x))^3 \left(\text{f0}(x)^2 y(x)^2-\text{f1}(x)^2\right)-2 y(x) (1-y(x)) y''(x)+(1-3 y(x)) y'(x)^2=0