4.18.4 $x{y}^{\prime }(x{)}^2+4y^{\prime }(x)-2y(x)=0$

ODE
$$x{y}^{\prime }(x{)}^2+4y^{\prime }(x)-2y(x)=0$$ ODE Classification

[_rational, _dAlembert]

Book solution method
No Missing Variables ODE, Solve for $x$

Mathematica ✓
cpu = 30.997 (sec), leaf count = 40

$$\text{Solve}[\{\text{K}\mathrm{\$}\text{1655}x+4=\frac{2y(\text{K}\mathrm{\$}\text{1655})}{\text{K}\mathrm{\$}\text{1655}},y(x)=\frac{\text{K}\mathrm{\$}\text{1655}(c_1\text{K}\mathrm{\$}\text{1655}+4\text{K}\mathrm{\$}\text{1655}\log (\text{K}\mathrm{\$}\text{1655})+8)}{(\text{K}\mathrm{\$}\text{1655}-2{)}^2}\},\{y(x),\text{K}\mathrm{\$}\text{1655}\}]$$

Maple ✓
cpu = 0.019 (sec), leaf count = 43

$$\{[x\left(\mathit{\_}\mathit{T}\right)=\frac{-4\mathit{\_}\mathit{T}+8\ln \left(\mathit{\_}\mathit{T}\right)+\mathit{\_}\mathit{C}\mathit{1}}{{(-2+\mathit{\_}\mathit{T})}^2},y\left(\mathit{\_}\mathit{T}\right)=\frac{\mathit{\_}\mathit{T}(8\mathit{\_}\mathit{T}\ln \left(\mathit{\_}\mathit{T}\right)+16+(\mathit{\_}\mathit{C}\mathit{1}-16)\mathit{\_}\mathit{T})}{2{(-2+\mathit{\_}\mathit{T})}^2}]\}$$ Mathematica raw input

DSolve[-2*y[x] + 4*y'[x] + x*y'[x]^2 == 0,y[x],x]

Mathematica raw output

Solve[{4 + K$1655*x == (2*y[K$1655])/K$1655, y[x] == (K$1655*(8 + K$1655*C[1] + 
4*K$1655*Log[K$1655]))/(-2 + K$1655)^2}, {y[x], K$1655}]

Maple raw input

dsolve(x*diff(y(x),x)^2+4*diff(y(x),x)-2*y(x) = 0, y(x),'implicit')

Maple raw output

[x(_T) = 1/(-2+_T)^2*(-4*_T+8*ln(_T)+_C1), y(_T) = 1/2*_T*(8*_T*ln(_T)+16+(_C1-1
6)*_T)/(-2+_T)^2]