  Let $R$ be a $\mathbb{Q}$-algebra and $d$ be a locally nilpotent derivation
on $R$. We will show that the Jacobson radical of a differential polynomial
ring $R[x;d]$ equals $I[x;d]$ where $I$ is a nil ideal of $R$. This answers a
question posed by Agata Smoktunowicz.
