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Find the amount in a savings aacount after one year if the initial balance in the account was $1,000, if the interest is paid continuously into the account at a nominal rate of 10% per annum, compounded continuously, and if the account is being continuously depleted at the rate of y^2/1000000 dollars per year, where y=y(t) is the balance in the account after t years. How large can the account grow? How long will it take the account grow to half this balance?

Just like other problems of this sort, I set up the following equation:

dy/dt=0.1y-y^2/1000000

integrating factor u(t)

dy/dt*u(t)=0.1y*u(t)-y^2/1000000*u(t)

d/dt(yu(t))=dy/dt*u(t)+du/dt*y

now, what do I do? I have never done a question involving y^2. Help, please!!

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# Financial model using integral

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