\[ \boxed { x \left ( {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) \right ) \ln \left ( x \right ) +y \left ( x \right ) -ax \left ( \ln \left ( x \right ) +1 \right ) =0} \]
Mathematica: cpu = 0.007501 (sec), leaf count = 16 \[ \left \{\left \{y(x)\to a x+\frac {c_1}{\log (x)}\right \}\right \} \]
Maple: cpu = 0.0 (sec), leaf count = 14 \[ \left \{ y \left ( x \right ) =ax+{\frac {{\it \_C1}}{\ln \left ( x \right ) }} \right \} \]