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