ODE
\[ x \log (x) y'(x)=a x (\log (x)+1)-y(x) \] ODE Classification
[_linear]
Book solution method
Linear ODE
Mathematica ✓
cpu = 0.180378 (sec), leaf count = 16
\[\left \{\left \{y(x)\to a x+\frac {c_1}{\log (x)}\right \}\right \}\]
Maple ✓
cpu = 0.013 (sec), leaf count = 14
\[\left [y \left (x \right ) = a x +\frac {\textit {\_C1}}{\ln \left (x \right )}\right ]\] 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))
Maple raw output
[y(x) = a*x+1/ln(x)*_C1]