ODE
\[ x y'(x)=y(x) \log (y(x)) \] ODE Classification
[_separable]
Book solution method
Separable ODE, Neither variable missing
Mathematica ✓
cpu = 0.222282 (sec), leaf count = 13
\[\left \{\left \{y(x)\to e^{e^{c_1} x}\right \}\right \}\]
Maple ✓
cpu = 0.056 (sec), leaf count = 8
\[[y \left (x \right ) = {\mathrm e}^{x \textit {\_C1}}]\] Mathematica raw input
DSolve[x*y'[x] == Log[y[x]]*y[x],y[x],x]
Mathematica raw output
{{y[x] -> E^(E^C[1]*x)}}
Maple raw input
dsolve(x*diff(y(x),x) = y(x)*ln(y(x)), y(x))
Maple raw output
[y(x) = exp(x*_C1)]