PS6: Problem 14 Previous Problem Problem List Next Problem (1 point) Which of the following are separable differential equations? DA. dy = (3:+2y) dy B. di = sin(cy) UC. dy =cty D. y In(I) dy di I DE. dy = VItry 1 OF. x(1 + y?) Edx = y(1 + x2) 2dyPS6: Problem 15 Previous Problem Problem List Next Problem (1 point) Another model for a growth function for a limited population is given by the Gompertz function, which is a solution to the differential equation dP cln dt F P where c is a constant and K is the carrying capacity. Answer the following questions. 1. Solve the differential equation with a constant c = 0.1, carrying capacity K = 2000, and initial population Po = 1000. Answer: P(t) = 2. With c = 0.1, K = 2000, and Po = 1000, find lim P(t). 1-+00 Limit:PS6: Problem 16 Previous Problem Problem List Next Problem (1 point) A very large tank initially contains 100 of pure water. Starting at time t = 0 a solution with a salt concentration of 0.4kg/L is added at a rate of 61/min. The solution is kept thoroughly mixed and is drained from the tank at a rate of 4L/ min. Answer the following questions. 1. Let y(t) be the amount of salt (in kilograms) in the tank after t minutes. What differential equation does y satisfy? Use the variable y for y(t). dy Answer (in kilograms per minute): it 2. How much salt is in the tank after 50 minutes? Answer (in kilograms):PS6: Problem 17 Previous Problem Problem List Next Problem (1 point) For the linear differential equation y' + 5xy = c'e 2 the integrating factor is: After multiplying both sides by the integrating factor and unapplying the product rule we get the new differential equation: = Integrating both sides we get the algebraic equation Solving for y, the solution to the differential equation is y = (using k as the constant)PS6: Problem 18 Previous Problem Problem List Next Problem (1 point) Solve the initial-value problem to dy + 3y = t', t > 0, y(1) = 3. dt Answer: y(t) =