4.15.30 \(\left (x-2 \sqrt {x y(x)}\right ) y'(x)=y(x)\)

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 = 0.0885838 (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 = 0.034 (sec), leaf count = 18

\[ \left \{ \ln \left (y \relax (x ) \right ) +{x{\frac {1}{\sqrt {xy \relax (x ) }}}}-{\it \_C1}=0 \right \} \] 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),'implicit')

Maple raw output

ln(y(x))+1/(x*y(x))^(1/2)*x-_C1 = 0