Let y=y(t) be a solution of the differential equation (d y)/(d t)+α y=γ e^-β t where, α>0, β>0 and γ>0. Then lim_t → ∞ y(t)

Let $\displaystyle y=y(t)$ be a solution of the differential equation $$\frac{d y}{d t}+\alpha y=\gamma e^{-\beta t} $$ where, $\displaystyle \alpha>0, \beta>0$ and $\displaystyle \gamma>0$. Then $\displaystyle \lim _{t \rightarrow \infty} y(t)$