# Math Help - Applied DE

1. ## 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

2. ## 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 $\displaystyle k$.