Please read the information above to answer the question below. It deals with differential equations. If correct I will thumbs up. Thank you!

This project explores the how differential equations appear in economics. Two of the most basic concepts in economics are supply and demand. If a product is to be sold at price p, then D(p) (the demand) is the total quantity that will be sold. The law of demand says that the demand will decrease as the price increases. If a product is to be sold at price p, then S(p) (the supply) is the total number that sellers will supply. The law of supply says that the supply will increase as the price increases. 9 = DCP) Quantity Quantity 9 = SCP) Price Price If the demand for a product is greater than the supply, then the price will go up. If the supply is greater than the demand then the price will go down. Said succinctly D(p) - S(p) > 0= dp > 0 dt D(P) - S(p) o. Throughout this project we assume that the price function, p(t) satisfies this differential equation. NO Project: Supply and Demand 1. Let's assume that both the demand and supply are linear functions with respect to price. More explicitly, let D(p) = 4 -p and S(p) = 1 + p. Find a general solution for the price as a function of time (it will involve k). What is the long term behaviour of the price? Does it tend to a specific value regardless of the initial price