## Separable Linear Equations

Hey guys,

I need some help with this one here:

Payments are made continuously on a mortgage of original amount P(subzero) dollars at the constant rate of c dollars per month. Let P(t) denote the balance (amount still owed) by the mortgage holder. (For example, r=0.06/12=0.005 if the annual interest rate is 6%).

dP/dt=rP-c

P(0)=P(subzero)

A) Derive the differential equation.

B) Solve the equation and determine the formula for the mortgage balance at time t.

C) Use formula found in (B) to compute the monthly payment on an N-year mortgage.