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We present and experimentally realize a quantum algorithm for efficiently solving the following problem: given an $N\times N$ matrix $\mathcal{M}$, an $N$-dimensional vector $\textbf{\emph{b}}$, and an initial vector $\textbf{\emph{x}}(0)$, obtain a target vector $\textbf{\emph{x}}(t)$ as a function of time $t$ according to the constraint $d\textbf{\emph{x}}(t)/dt=\mathcal{M}\textbf{\emph{x}}(t)+\textbf{\emph{b}}$.
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