ODE
\[ \left (x-2 \sqrt {x y(x)}\right ) y'(x)=y(x) \] ODE Classification
[[_homogeneous, `class A`], _dAlembert]
Book solution method
Homogeneous equation
Mathematica ✓
cpu = 0.502259 (sec), leaf count = 28
\[\text {Solve}\left [2 \left (\frac {1}{\sqrt {\frac {y(x)}{x}}}+\log \left (\frac {y(x)}{x}\right )+\log (x)\right )=c_1,y(x)\right ]\]
Maple ✓
cpu = 0.044 (sec), leaf count = 18
\[\left [\ln \left (y \left (x \right )\right )+\frac {x}{\sqrt {x y \left (x \right )}}-\textit {\_C1} = 0\right ]\] 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))
Maple raw output
[ln(y(x))+1/(x*y(x))^(1/2)*x-_C1 = 0]