How to solve the differential equation in $\mathcal{D'}(\mathbb{R})$:
\begin{equation} T''=\delta_a \Leftrightarrow \langle T'',\phi\rangle=\langle \delta_a,\phi''\rangle, \forall \phi \in \mathcal{D}(\mathbb{R}) \end{equation}
By now, I know how to solve the DE: \begin{equation} T'=\delta_a \end{equation}
but how should I proceed for the other one?
Thank you!