ODE
\[ x y'(x)=x^n \log (x)-y(x) \] ODE Classification
[_linear]
Book solution method
Linear ODE
Mathematica ✓
cpu = 0.0206706 (sec), leaf count = 29
\[\left \{\left \{y(x)\to \frac {c_1}{x}+\frac {x^n ((n+1) \log (x)-1)}{(n+1)^2}\right \}\right \}\]
Maple ✓
cpu = 0.014 (sec), leaf count = 31
\[ \left \{ y \left ( x \right ) ={\frac {{x}^{n}\ln \left ( x \right ) }{n+1}}-{\frac {{x}^{n}}{ \left ( n+1 \right ) ^{2}}}+{\frac {{\it \_C1}}{x}} \right \} \] Mathematica raw input
DSolve[x*y'[x] == x^n*Log[x] - y[x],y[x],x]
Mathematica raw output
{{y[x] -> C[1]/x + (x^n*(-1 + (1 + n)*Log[x]))/(1 + n)^2}}
Maple raw input
dsolve(x*diff(y(x),x) = x^n*ln(x)-y(x), y(x),'implicit')
Maple raw output
y(x) = 1/(n+1)*ln(x)*x^n-x^n/(n+1)^2+1/x*_C1