4.5.18 \(x y'(x)=y(x) \log (y(x))\)

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

\[ \left \{ \ln \relax (x ) -\ln \left (\ln \left (y \relax (x ) \right ) \right ) +{\it \_C1}=0 \right \} \] 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