ODE
\[ x y'(x)=y(x) \log (y(x)) \] ODE Classification
[_separable]
Book solution method
Separable ODE, Neither variable missing
Mathematica ✓
cpu = 0.00943726 (sec), leaf count = 13
\[\left \{\left \{y(x)\to e^{e^{c_1} x}\right \}\right \}\]
Maple ✓
cpu = 0.006 (sec), leaf count = 13
\[ \left \{ \ln \left ( x \right ) -\ln \left ( \ln \left ( y \left ( x \right ) \right ) \right ) +{\it \_C1}=0 \right \} \] 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),'implicit')
Maple raw output
ln(x)-ln(ln(y(x)))+_C1 = 0