Let $y=y(t)$ be a solution of the differential equation $\frac{\mathrm{dy}}{\mathrm{dt}}+\alpha y=\gamma \mathrm{e}^{-\beta t}$ Where, $\alpha0, \beta0$ and $\gamma0$. Then $\lim _{t \rightarrow \infty} y(t)$ [JEE Main 2023, 25 Jan (Shift 2)]

Question

Let $y=y(t)$ be a solution of the differential equation $\frac{\mathrm{dy}}{\mathrm{dt}}+\alpha y=\gamma \mathrm{e}^{-\beta t}$ Where, $\alpha>0, \beta>0$ and $\gamma>0$. Then $\lim _{t \rightarrow \infty} y(t)$ [JEE Main 2023, 25 Jan (Shift 2)]

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Let \(y=y(t)\) be a solution of the differential equation \(\frac{\mathrm{dy}}{\mathrm{dt}}+\alpha y=\gamma \mathrm{e}^{…

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