ODE
\[ x y''(x)+y'(x)=x^n \] ODE Classification
[[_2nd_order, _missing_y]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.187994 (sec), leaf count = 24
\[\left \{\left \{y(x)\to \frac {x^{n+1}}{(n+1)^2}+c_1 \log (x)+c_2\right \}\right \}\]
Maple ✓
cpu = 0.214 (sec), leaf count = 44
\[\left [y \left (x \right ) = \frac {\textit {\_C1} \ln \left (x^{n +1}\right ) n}{\left (n +1\right )^{2}}+\frac {\textit {\_C1} \ln \left (x^{n +1}\right )}{\left (n +1\right )^{2}}+\frac {x^{n +1}}{\left (n +1\right )^{2}}+\textit {\_C2}\right ]\] Mathematica raw input
DSolve[y'[x] + x*y''[x] == x^n,y[x],x]
Mathematica raw output
{{y[x] -> x^(1 + n)/(1 + n)^2 + C[2] + C[1]*Log[x]}}
Maple raw input
dsolve(x*diff(diff(y(x),x),x)+diff(y(x),x) = x^n, y(x))
Maple raw output
[y(x) = 1/(n+1)^2*_C1*ln(x^(n+1))*n+1/(n+1)^2*_C1*ln(x^(n+1))+1/(n+1)^2*x^(n+1)+_C2]