ODE
\[ f\left (x y'(x),y(x)\right )=0 \] ODE Classification
[_separable]
Book solution method
Homogeneous ODE, The Isobaric equation
Mathematica ✓
cpu = 1.12419 (sec), leaf count = 28
\[\left \{\left \{y(x)\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}} \frac {1}{\text {InverseFunction}[f,1,2][0,K[1]]} \, dK[1]\& \right ]\left [c_1+\log (x)\right ]\right \}\right \}\]
Maple ✓
cpu = 0.016 (sec), leaf count = 22
\[ \left \{ \ln \left ( x \right ) -\int ^{y \left ( x \right ) }\!{\it RootOf} \left ( f \left ( {{\it \_Z}}^{-1},{\it \_a} \right ) \right ) {d{\it \_a}}-{\it \_C1}=0 \right \} \] Mathematica raw input
DSolve[f[x*y'[x], y[x]] == 0,y[x],x]
Mathematica raw output
{{y[x] -> InverseFunction[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),'implicit')
Maple raw output
ln(x)-Intat(RootOf(f(1/_Z,_a)),_a = y(x))-_C1 = 0