ODE
\[ x y''(x)+y'(x)=x^n \] ODE Classification
[[_2nd_order, _missing_y]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.194637 (sec), leaf count = 24
\[\left \{\left \{y(x)\to c_1 \log (x)+c_2+\frac {x^{n+1}}{(n+1)^2}\right \}\right \}\]
Maple ✓
cpu = 0.126 (sec), leaf count = 37
\[ \left \{ y \left ( x \right ) ={\frac {{\it \_C1}\, \left ( n+1 \right ) \ln \left ( {x}^{n+1} \right ) +{\it \_C2}\,{n}^{2}+2\,{\it \_C2}\,n+{\it \_C2}+{x}^{n+1}}{ \left ( n+1 \right ) ^{2}}} \right \} \] 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),'implicit')
Maple raw output
y(x) = (_C1*(n+1)*ln(x^(n+1))+_C2*n^2+2*_C2*n+_C2+x^(n+1))/(n+1)^2