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