4.3.35 \(y'(x)+y(x) \log (x) \log (y(x))=0\)

ODE
\[ y'(x)+y(x) \log (x) \log (y(x))=0 \] ODE Classification

[_separable]

Book solution method
Separable ODE, Neither variable missing

Mathematica
cpu = 0.0168001 (sec), leaf count = 19

\[\left \{\left \{y(x)\to e^{x^{-x} e^{c_1+x}}\right \}\right \}\]

Maple
cpu = 0.007 (sec), leaf count = 16

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

DSolve[Log[x]*Log[y[x]]*y[x] + y'[x] == 0,y[x],x]

Mathematica raw output

{{y[x] -> E^(E^(x + C[1])/x^x)}}

Maple raw input

dsolve(diff(y(x),x)+y(x)*ln(x)*ln(y(x)) = 0, y(x),'implicit')

Maple raw output

x*ln(x)-x+ln(ln(y(x)))+_C1 = 0