Let y = y(t) be a solution of the differential equation dy/dx + αy = γe^{-βt}

Question

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

Where, α > 0, β > 0 and γ > 0. Then \(\lim\limits_{t\to \infty} y(t)\)

(1) is 0

(2) does not exist

(3) is 1

(4) is –1

Answer 1

Correct option is (1) is 0