2.506   ODE No. 506

1. Problem in Latex
2. Mathematica input
3. Maple input

$$2x^2(y(x)-x)y(x{)}^2{y}^{\prime }(x)+x^2(xy(x{)}^2-1)y^{\prime }(x{)}^2-(x^{2}y(x)-1)y(x{)}^2=0$$ ✗ Mathematica : cpu = 61.7738 (sec), leaf count = 0 , could not solve

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

✗ Maple : cpu = 0. (sec), leaf count = 0 , could not solve

dsolve(x^2*(x*y(x)^2-1)*diff(y(x),x)^2+2*x^2*y(x)^2*(y(x)-x)*diff(y(x),x)-y(x)^2*(x^2*y(x)-1)=0,y(x))