ODE No. 484

$$(2xy(x)-x^2)y^{\prime }(x{)}^2-6xy(x)y^{\prime }(x)-y(x{)}^2+2xy(x)=0$$ ✓ Mathematica : cpu = 0.172743 (sec), leaf count = 81

DSolve[2*x*y[x] - y[x]^2 - 6*x*y[x]*Derivative[1][y][x] + (-x^2 + 2*x*y[x])*Derivative[1][y][x]^2 == 0,y[x],x]
 

$$\{\{y(x)\to -\sqrt{3x^2-2e^{\frac{c_1}{2}}x}+2x-e^{\frac{c_1}{2}}\},\{y(x)\to \sqrt{3x^2-2e^{\frac{c_1}{2}}x}+2x-e^{\frac{c_1}{2}}\}\}$$ ✓ Maple : cpu = 0.09 (sec), leaf count = 115

dsolve((2*x*y(x)-x^2)*diff(y(x),x)^2-6*x*y(x)*diff(y(x),x)-y(x)^2+2*x*y(x) = 0,y(x))
 

$$y\left(x\right)=0$$