Problems

In Problems 1-10, find the general solution of the given differential equation.

In Problems 11-14, find the general solution using the definite integral form when the integral cannot be evaluated.

15            A population has a net birthrate of 2.5 % per year and a net annual immigration equal to 10,000t - 40,000, where t is measured in years. At time t = 0, the population is y(0) = 100,000. Find the population as a function of t.

16            Work Problem 15 if the net annual immigration is 1,000(cos t - 1).

17            A bank account earns interest at the rate of 10% per year, and money is deposited continuously into the account at the rate of 5t² dollars per year. The earnings due to interest are also left in the account. If the account had $5000 at time t = 0 years, find the amount in the account at time t = 10 years.

18            Work Problem 17 if there are no deposits but money is withdrawn continuously from the account at the rate of 5t² dollars per year.

19            Use differential equations to prove the capital accumulation formula in Section 8.4. The formula says that if money is deposited continuously in an account at the rate of f(t) dollars per year, and the account earns interest at the annual rate r, and there are zero dollars in the account at time t = a, then the value of the account at time t = b will be