ODE
\[ f\left (x y'(x),y(x)\right )=0 \] ODE Classification
[_separable]
Book solution method
Homogeneous ODE, The Isobaric equation
Mathematica ✓
cpu = 0.172661 (sec), leaf count = 29
\[\left \{\left \{y(x)\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}}\frac {1}{\text {InverseFunction}[f,1,2][0,K[1]]}dK[1]\& \right ][\log (x)+c_1]\right \}\right \}\]
Maple ✓
cpu = 0.133 (sec), leaf count = 22
\[\left [\ln \left (x \right )-\left (\int _{}^{y \left (x \right )}\RootOf \left (f \left (\frac {1}{\textit {\_Z}}, \textit {\_a}\right )\right )d \textit {\_a} \right )-\textit {\_C1} = 0\right ]\] Mathematica raw input
DSolve[f[x*y'[x], y[x]] == 0,y[x],x]
Mathematica raw output
{{y[x] -> InverseFunction[Inactive[Integrate][InverseFunction[f, 1, 2][0, K[1]]^(-1), {K[1], 1, #1}] & ][C[1] + Log[x]]}}
Maple raw input
dsolve(f(x*diff(y(x),x),y(x)) = 0, y(x))
Maple raw output
[ln(x)-Intat(RootOf(f(1/_Z,_a)),_a = y(x))-_C1 = 0]