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**[SOLVED] Personal Wealth Model using DE's**

Hey, I am having trouble with this question.

Most people have an income that comes from 2 sources: salary and personal investments. From this income, 'necessary' expenses (housing, food) are paid, some money is spent on luxuries and the rest is saved (increasing investments).

Given that income must equal outflow, show the steps in developing the following mathematics model for a person's wealth at any time t:

dW/dt=(1-p)(s-n+rW)

Where s= your salary

W(t)= your wealth (savings), which is a function of time

r= rate of interest on your wealth (savings)

n= amount spent on necessities

p=proportion of your income after necessities that you spend on luxuries.

Ok what I have to try to figure out is how to differentiate this model (if possible) to get it to the form of:

W(t)=((s-n)/r)(e^((1-p)rt)-1)

I'm not sure whether this is sufficient information as I left what appeared to be a lot of irrelevant information out.

Thanks very much for your help.