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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- Aug 16th 2011, 07:28 AMdecoy808Applied 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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http://i56.tinypic.com/2zsutm0.jpg - Aug 16th 2011, 07:52 AMProve ItRe: Applied DE
Well for (i), if $\displaystyle \displaystyle \frac{dy}{dt}$ is proportional to the product of $\displaystyle \displaystyle x$ and $\displaystyle \displaystyle y$, then

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

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