\[ a (1-y(x))^2 (x-y(x))^2 y(x)^2+b x (1-y(x))^2 (x-y(x))^2-c (1-x) (x-y(x))^2 y(x)^2-d (1-x) x (1-y(x))^2 y(x)^2+2 (1-x)^2 x^2 (1-y(x)) (x-y(x)) y(x) y''(x)-(1-x)^2 x^2 \left (3 y(x)^2-2 x y(x)-2 y(x)+x\right ) y'(x)^2-2 (1-x) x (1-y(x)) y(x) \left (x^2-2 x y(x)+y(x)\right ) y'(x)=0 \] ✗ Mathematica : cpu = 28.6783 (sec), leaf count = 0 , could not solve
DSolve[b*x*(1 - y[x])^2*(x - y[x])^2 - d*(1 - x)*x*(1 - y[x])^2*y[x]^2 - c*(1 - x)*(x - y[x])^2*y[x]^2 + a*(1 - y[x])^2*(x - y[x])^2*y[x]^2 - 2*(1 - x)*x*(1 - y[x])*y[x]*(x^2 + y[x] - 2*x*y[x])*Derivative[1][y][x] - (1 - x)^2*x^2*(x - 2*y[x] - 2*x*y[x] + 3*y[x]^2)*Derivative[1][y][x]^2 + 2*(1 - x)^2*x^2*(1 - y[x])*(x - y[x])*y[x]*Derivative[2][y][x] == 0, y[x], x]
✗ Maple : cpu = 0. (sec), leaf count = 0 , could not solve
dsolve(2*x^2*y(x)*(1-x)^2*(1-y(x))*(x-y(x))*diff(diff(y(x),x),x)-x^2*(1-x)^2*(x-2*x*y(x)-2*y(x)+3*y(x)^2)*diff(y(x),x)^2-2*x*y(x)*(1-x)*(1-y(x))*(x^2+y(x)-2*x*y(x))*diff(y(x),x)+b*x*(1-y(x))^2*(x-y(x))^2-c*(1-x)*y(x)^2*(x-y(x))^2-d*x*y(x)^2*(1-x)*(1-y(x))^2+a*y(x)^2*(x-y(x))^2*(1-y(x))^2=0,y(x))