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

Step-by-step solution

Given, d y d t + α y = γ · e - β t Which is a linear differential equation, So, integrating factor will be I . F = e ∫ α d t = e α t So, the solution of differential equation is given by y × e α t = γ ∫ e - β t × e α t ⇒ y × e α t = γ ∫ e α - β t ⇒ y × e α t = γ e α - β t α - β + c ⇒ y = γ e - β t α - β + c e - α t Now finding lim t &#85