ODE
\[ y'(x)+y(x) \log (x) \log (y(x))=0 \] ODE Classification
[_separable]
Book solution method
Separable ODE, Neither variable missing
Mathematica ✓
cpu = 0.225672 (sec), leaf count = 19
\[\left \{\left \{y(x)\to e^{x^{-x} e^{x+c_1}}\right \}\right \}\]
Maple ✓
cpu = 0.198 (sec), leaf count = 16
\[\left [y \left (x \right ) = {\mathrm e}^{\frac {x^{-x} {\mathrm e}^{x}}{\textit {\_C1}}}\right ]\] 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))
Maple raw output
[y(x) = exp(x^(-x)/_C1*exp(x))]