Inverse Laplace transform problem 1

Hello,

I got the following differential equation :

$\displaystyle E_2'(t)+2{}E_2(t) = E_1(t) + E_1'(t)$

Transforming this into a Laplace equation and computing the transfer function, I get :

$\displaystyle H(s) = {{s+1} \over {s+2}}$

Where I get into trouble is to obtain the inverse transformation. It seems probably silly. I do not have any problem solving more complex equations using partial fractions, but trying, this does not seem to apply here :

$\displaystyle {{s+1} \over {s+2}} = {A \over {s+2}}$

(Headbang)

What am I missing here?

Thanks,

Jurgen

Reply : Inverse Laplace transform problem 1

Why not? I have controlled the answer above yours, which says

$\displaystyle \displaystyle \frac{s+1}{s+2}= 1-\frac{1}{s+2}$

which then translates to

$\displaystyle \delta{(t)}-e^{-2t}$