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26 September, 12:52

Given dy/dt=4y and y (2) = 400. Find y (7).

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  1. 26 September, 13:36
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    For us to find the value of y at t equal to 7, we need to integrate first the differential equation given above. It is a variable separable equation so we can easily integrate it as follows:

    dy/dt = 4y

    dy/4y = dt

    (integral) dy/4y = (integral) dt

    (1/4) ln (y) + C = t

    To determine C, we substitute y (2) = 400

    (1/4) ln (400) + C = 2

    C = 0.5

    Find y (7).

    (1/4) ln (y) + 0.5 = t

    (1/4) ln (y) + 0.5 = 7

    (1/4) ln (y) = 6.5

    ln (y) = 26

    e^ln (y) = e^26

    y = 1.96x10^11
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