a (1-y(x))^2 (x-y(x))^2 y(x)^2+b x (1-y(x))^2 (x-y(x))^2-c (1-x) (x-y(x))^2 y(x)^2-d (1-x) x (1-y(x))^2 y(x)^2+2 (1-x)^2 x^2 (1-y(x)) (x-y(x)) y(x) y''(x)-(1-x)^2 x^2 \left(3 y(x)^2-2 x y(x)-2 y(x)+x\right) y'(x)^2-2 (1-x) x (1-y(x)) y(x) \left(x^2-2 x y(x)+y(x)\right) y'(x)=0