ODE
\[ y(x) f\left (\frac {y'(x)}{y(x)},x\right )=0 \] ODE Classification
[_separable]
Book solution method
Homogeneous ODE, equation of form \(y f(x , \frac {y'}{y})\)
Mathematica ✓
cpu = 0.169738 (sec), leaf count = 29
\[\left \{\{y(x)\to 0\},\left \{y(x)\to c_1 \exp \left (\int _1^x\text {InverseFunction}[f,1,2][0,K[1]]dK[1]\right )\right \}\right \}\]
Maple ✓
cpu = 0.224 (sec), leaf count = 17
\[[y \left (x \right ) = 0, y \left (x \right ) = \textit {\_C1} \,{\mathrm e}^{\int \RootOf \left (f \left (\textit {\_Z} , x\right )\right )d x}]\] Mathematica raw input
DSolve[f[y'[x]/y[x], x]*y[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> 0}, {y[x] -> E^Inactive[Integrate][InverseFunction[f, 1, 2][0, K[1]], {K[1], 1, x}]*C[1]}}
Maple raw input
dsolve(y(x)*f(diff(y(x),x)/y(x),x) = 0, y(x))
Maple raw output
[y(x) = 0, y(x) = _C1*exp(Int(RootOf(f(_Z,x)),x))]