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3.2.1 а) е) Exercises In the first three problems, set up but do not solve the system of differen- tial equations and/or initial value problem (IVP) whose solution would give the amount of salt in each tank at time t. Write each system in matrix form. Exercise 3.1.1. A system of two tanks is connected such that each tank has independent inflows and outflows (drains), and each tank is connected to the other with an inflow and an outflow. The relevant information about each tank is given in the table below Tank volume Rate of inflow to the tank Rate of drain outflow Rate of outflow to other tankto B: 2 L/min to A:1 L/min Concentration of salt in inflow 6g/L Tank A 200 L 5 L/min 4 L/min Tank B 250 L 7 L/min 8 L/min Exercise 3.1.2. The situation is the same as in Exercise 3.1.1, except now the concen tration of salt in the inflow of tank A is5+cos(2t) g/L, and the concentration of sal in the inflow of tank B is 9+2e g/L. Furthermore, the concentration of the solute in tank A is initially 7 g/L, and tank B initially contains 225 g of salt Exercise 3.1.3. For a closed system of three tanks(i.e., there are no external input Joutput lows for any of the tanks), the following information is given Tank A Tank B Tank C Tank volume 350 L 100 L 400 L Rate ofontflou, 1 to B: 3 L/inin | to C: OL/min | to A: OL/min Rate of outflow to C: 5 L/min to A: 8 L/min to B:5 L/min Tank A initially has 600 g of salt in the tank, the concentration of solute in ta initially 17 g/L, and the concentration of solute in tank C is initially 8 g/L Exercise 3.2.1. Reurite the following highey order ODEs as an equivalent frst order system. Write each system in matrix form. b) y'+4y-12-e -ey+5y-tan(t)y 12 cos(4t)

Answer 1

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