4.15.30 $(x-2\sqrt{xy(x)})y^{\prime }(x)=y(x)$

ODE
$$(x-2\sqrt{xy(x)})y^{\prime }(x)=y(x)$$ ODE Classification

[[_homogeneous, `class A`], _dAlembert]

Book solution method
Homogeneous equation

Mathematica ✓
cpu = 0.0885838 (sec), leaf count = 28

$$\text{Solve}[2(\frac{1}{\sqrt{\frac{y(x)}{x}}}+\log \left(\frac{y(x)}{x}\right)+\log (x))=c_1,y(x)]$$

Maple ✓
cpu = 0.034 (sec), leaf count = 18

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

DSolve[(x - 2*Sqrt[x*y[x]])*y'[x] == y[x],y[x],x]

Mathematica raw output

Solve[2*(Log[x] + Log[y[x]/x] + 1/Sqrt[y[x]/x]) == C[1], y[x]]

Maple raw input

dsolve((x-2*(x*y(x))^(1/2))*diff(y(x),x) = y(x), y(x),'implicit')

Maple raw output

ln(y(x))+1/(x*y(x))^(1/2)*x-_C1 = 0