Mr. Brown has taken out a loan of value $1,000 with a 5% APR. He has been paying off the loan at a constant rate of r = $150/year. Set up a linear ODE for the balance of the loan P(t) as a function of time t in years. [If you're having trouble getting started, please see Example 2 from

Answer:[tex]\frac{dp}{dt}[/tex] = 0.05P - 150Step-by-step explanation:Let P(t) be the balance of the loan at time t years,Let P(t) will satisfy [tex]\frac{dp}{dt}=rP-R[/tex]where r = annual interest rate           R = per year payment rate           R = $150/year           r = [tex]\frac{5}{100}[/tex] = 0.05  [tex]\frac{5}{100}[/tex]Now we have the following picture,Interest            Balance          Payment5%           ⇒          P(t)       ⇒     $150/year(0.05)Therefore, a linear ODE satisfied by P(t) is given by[tex]\frac{dp}{dt}[/tex] = 0.05P - 150