\[ -a x (\log (x)+1)+x \log (x) y'(x)+y(x)=0 \] ✓ Mathematica : cpu = 0.027725 (sec), leaf count = 16
DSolve[-(a*x*(1 + Log[x])) + y[x] + x*Log[x]*Derivative[1][y][x] == 0,y[x],x]
\[\left \{\left \{y(x)\to a x+\frac {c_1}{\log (x)}\right \}\right \}\] ✓ Maple : cpu = 0.008 (sec), leaf count = 14
dsolve(x*diff(y(x),x)*ln(x)+y(x)-a*x*(ln(x)+1) = 0,y(x))
\[y \left (x \right ) = a x +\frac {c_{1}}{\ln \left (x \right )}\]