differential equations

Question

A very large tank initially contains 100L100L of pure water. Starting at time 𝑡=0t=0 a solution with a salt concentration of 0.5kg/L0.5kg/L is added at a rate of 6L/min.6L/min. The solution is kept thoroughly mixed and is drained from the tank at a rate of 4L/min.4L/min. Answer the following questions.

1. Let 𝑦(𝑡)y(t) be the amount of salt (in kilograms) in the tank after 𝑡t minutes. What differential equation does 𝑦ysatisfy? Use the variable 𝑦y for 𝑦(𝑡).y(t). 

Answer (in kilograms per minute): 𝑑𝑦𝑑𝑡=dydt= 2. How much salt is in the tank after 2020 minutes? 

Answer (in kilograms): 

Answer 1

d y / dt = (0.5)·( 6 ) − y / [ 100 + (6−4)· t ]

WHICH IS A LINEAR OF FIRST ORDER