# differential equation with distributions

I'm stuggeling with this differential equation:

$T'+T=0$

Where $T$ is distribution.

I found solutions in form:

$\sum_{n\in A} \frac{d^n}{dx^n}\Lambda_{c_n e^{-x}}$. This can be simplified to $\sum_{n\in A} \Lambda_{b_n e^{-x}}$.

Where $A \subset \mathbb{N}_0$ finite, $c_n,b_n$ arbitrary. But I don't know if I found all solutions.

What is $\Lambda$? –  Davide Giraudo Feb 4 '13 at 14:55