Hi!

Problem:$\displaystyle (1) \; \; y_{n+1}-y_{n}=e^{n} \; , y_{0}=0 $

Solution:Characteristic equation: $\displaystyle r-1=0 $ .

$\displaystyle r = 1 $

$\displaystyle y_{n}^{h} = C_{1}\cdot 1^{n} $

Particular solution: $\displaystyle y_{n}^{p}=An\cdot e^{n} $ <-- Is this correct ?

When I insert this into (1) I get, $\displaystyle e^{n}\left[A(n+1)\cdot e - An\right] = e^{n} $

Thx