ODE
\[ (x+1) y'(x)=n y(x)+e^x (x+1)^{n+1} \] ODE Classification
[_linear]
Book solution method
Linear ODE
Mathematica ✓
cpu = 0.201617 (sec), leaf count = 17
\[\left \{\left \{y(x)\to \left (e^x+c_1\right ) (x+1)^n\right \}\right \}\]
Maple ✓
cpu = 0.014 (sec), leaf count = 14
\[[y \left (x \right ) = \left ({\mathrm e}^{x}+\textit {\_C1} \right ) \left (1+x \right )^{n}]\] Mathematica raw input
DSolve[(1 + x)*y'[x] == E^x*(1 + x)^(1 + n) + n*y[x],y[x],x]
Mathematica raw output
{{y[x] -> (1 + x)^n*(E^x + C[1])}}
Maple raw input
dsolve((1+x)*diff(y(x),x) = exp(x)*(1+x)^(n+1)+n*y(x), y(x))
Maple raw output
[y(x) = (exp(x)+_C1)*(1+x)^n]