ODE
\[ x \log (x) y'(x)=a x (\log (x)+1)-y(x) \] ODE Classification
[_linear]
Book solution method
Linear ODE
Mathematica ✓
cpu = 0.00652861 (sec), leaf count = 16
\[\left \{\left \{y(x)\to a x+\frac {c_1}{\log (x)}\right \}\right \}\]
Maple ✓
cpu = 0.006 (sec), leaf count = 14
\[ \left \{ y \left ( x \right ) =ax+{\frac {{\it \_C1}}{\ln \left ( x \right ) }} \right \} \] Mathematica raw input
DSolve[x*Log[x]*y'[x] == a*x*(1 + Log[x]) - y[x],y[x],x]
Mathematica raw output
{{y[x] -> a*x + C[1]/Log[x]}}
Maple raw input
dsolve(diff(y(x),x)*x*ln(x) = a*x*(1+ln(x))-y(x), y(x),'implicit')
Maple raw output
y(x) = a*x+1/ln(x)*_C1