ODE
\[ x y'(x)=x^n \log (x)-y(x) \] ODE Classification
[_linear]
Book solution method
Linear ODE
Mathematica ✓
cpu = 0.19592 (sec), leaf count = 29
\[\left \{\left \{y(x)\to \frac {x^n ((n+1) \log (x)-1)}{(n+1)^2}+\frac {c_1}{x}\right \}\right \}\]
Maple ✓
cpu = 0.022 (sec), leaf count = 36
\[\left [y \left (x \right ) = \frac {x^{n} \ln \left (x \right )}{n +1}-\frac {x^{n}}{n^{2}+2 n +1}+\frac {\textit {\_C1}}{x}\right ]\] 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))
Maple raw output
[y(x) = x^n*ln(x)/(n+1)-x^n/(n^2+2*n+1)+1/x*_C1]