We can model the repayment of a mortgage with a differential equation. Suppose that y(t) is the amount still owed on the mortgage at time t, the rate of repayment per unit time is a, b is the interest rate, and that the initial amount of the mortgage is y0. 

(a) Find the differential equation for y(t). 

(b) Try a solution of the form y(t) = a/b + Cebt, where C is a constant to be determined from the initial conditions. Find C, plot the solution, and determine the time required to pay off the mortgage.

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