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17 April, 21:48

A calf that weighs x pounds at birth gains weight at the rate of dw/dt = 1200-w, where w is weight in pounds and t in time in years. Solve the differential equation.

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  1. 18 April, 00:01
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    W' = 1200 - w

    w'⋅ (e^t) + w⋅ (e^t) = 1200⋅ (e^t)

    w'⋅ (e^t) + w⋅ (d/dx e^t) = 1200⋅ (e^t)

    d/dt [ w⋅ (e^t) ] = 1200⋅ (e^t)

    ∫ d/dt [ w⋅ (e^t) ] dt = ∫ 1200⋅ (e^t) dt

    w⋅e^t = 1200⋅e^t + C

    w = [ 1200⋅e^t + C ] ⁄ e^t

    w = 1200 + C⋅e^ (-t)

    w_o = w (0) = 1200 + C⋅e^ (-0) = 1200 + C

    C = w_o - 1200

    w = 1200 + (w_o - 1200) ⋅e^ (-t)
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