4.40.23 $xy(x)y^{″}(x)+x{y}^{\prime }(x{)}^2+2y(x)y^{\prime }(x)=0$

ODE
$$xy(x)y^{″}(x)+x{y}^{\prime }(x{)}^2+2y(x)y^{\prime }(x)=0$$ ODE Classification

[[_2nd_order, _exact, _nonlinear], _Liouville, [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]

Book solution method
TO DO

Mathematica ✓
cpu = 0.0446592 (sec), leaf count = 24

$$\left\{\{y(x)\to \frac{c_2\sqrt{2-c_{1}x}}{\sqrt{x}}\}\right\}$$

Maple ✓
cpu = 0.016 (sec), leaf count = 18

$$\{\frac{{\left(y\left(x\right)\right)}^2}{2}+\frac{\mathit{\_}\mathit{C}\mathit{1}}{x}-\mathit{\_}\mathit{C}\mathit{2}=0\}$$ Mathematica raw input

DSolve[2*y[x]*y'[x] + x*y'[x]^2 + x*y[x]*y''[x] == 0,y[x],x]

Mathematica raw output

{{y[x] -> (Sqrt[2 - x*C[1]]*C[2])/Sqrt[x]}}

Maple raw input

dsolve(x*y(x)*diff(diff(y(x),x),x)+x*diff(y(x),x)^2+2*y(x)*diff(y(x),x) = 0, y(x),'implicit')

Maple raw output

1/2*y(x)^2+_C1/x-_C2 = 0