 Time-dependent-inflow convolution for a linear gas regulator

For ${\dot{M}}_g+ϵM_g=\Phi (t)$, multiplication by $e^{ϵt}$ and integration gives $M_g=M_0{e}^{-ϵt}+{\int }_0^t{e}^{-ϵ(t-s)}\Phi (s)ds$. Exponential memory filters the past inflow; the constant-inflow equilibrium is one specialization.