Question:

1. Solve \(\frac{dy}{dx}=2x{{y}^{2}}\), with \(y\left( 0 \right)=1\). What is when reaches infinity?
2. Find the general solution to
3. Use Euler’s Method with a step size of 0.5 to estimate y (2) if \(y'=xy-1\), where \(y\left( 1 \right)=2\)
4. A population of insects in a region will grow at a rate that is proportional to their current population. In the absence of the outside factors, the population will quadruple in two weeks time. On any given day there is a net migration into the area of 20 insects and 15 insects are eaten by a local bird and 10 insects die of natural causes. If there are initially 150 insects in the area, will the population survive? If not, when do they die out?

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Solution: The downloadable solution consists of 3 pages
Deliverable: Word Document