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Math Help - Applied DE

  1. #1
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    Applied DE

    Need help with a past exam questions for revision. could someone help me with the method for the questions or hint at what I need to do. many thanks




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  2. #2
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    Re: Applied DE

    Well for (i), if \displaystyle \frac{dy}{dt} is proportional to the product of \displaystyle x and \displaystyle y, then

    \displaystyle \frac{dy}{dx} = kxy = k\left[\frac{10}{(1 + t)^3}\right]y where \displaystyle k is some constant.

    Now use the fact that when \displaystyle t = 0, y = 20 and \displaystyle \frac{dy}{dt} = -40 to find \displaystyle k.
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