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MCQMediumJEE Main 2023 · 25 January, Shift 2Linear Differential Equations

Mathematics Question from JEE Main 2023 · 25 January, Shift 2

Let y=y(t)y = y(t) be a solution to the differential equation:

dydt+αy=γe−βt\frac{dy}{dt} + \alpha y = \gamma e^{-\beta t}

where α,β,γ>0\alpha, \beta, \gamma > 0. We are interested in finding the value of:

lim⁡t→∞y(t)\lim_{t \to \infty} y(t)

then:

  • A

    Is 00

  • B

    does not exist

  • C

    Is 11

  • D

    Is −1-1

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