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21 August, 03:51

Solve differential equation dy (t) / dt = - 2y (t) with initial condition y = 2 when t = 1

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  1. 21 August, 03:57
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    y = 2e^[2 (1 - t) ]

    Step-by-step explanation:

    1/y. dy = - 2. dt

    ln (y) = - 2t + c

    ln (2) = - 2 (1) + c

    c = 2 + ln (2)

    ln (y) = - 2t + ln (2) + 2

    ln (y) - ln (2) = 2 - 2t

    ln (y/2) = 2 - 2t

    y/2 = e^ (2 - 2t)

    y = 2e^[2 (1 - t) ]
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