ODE No. 490

$$a-x^2-2xy(x)y^{\prime }(x)+y(x{)}^2{y}^{\prime }(x{)}^2+2y(x{)}^2=0$$ ✓ Mathematica : cpu = 0.420323 (sec), leaf count = 70

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

$$\{\{y(x)\to -\frac{\sqrt{-a-2x^2+8c_{1}x-4c_1{}^2}}{\sqrt{2}}\},\{y(x)\to \frac{\sqrt{-a-2x^2+8c_{1}x-4c_1{}^2}}{\sqrt{2}}\}\}$$ ✓ Maple : cpu = 0.526 (sec), leaf count = 145

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

$$y\left(x\right)=-\frac{\sqrt{4x^2-2a}}{2}$$