Question

A. There are many methods for solving systems of differential equations using MATLAB. Here is a link to information regarding one method. B. Set up a system of equations for the following situation and then use MATLAB to solve the system. Tank A contains 50 gallons of water in which 25 pounds of salt are dissolved. A second tank, B, contains 50 gallons of pure water. Liquid is pumped in and out of the tanks at the rates shown in Figure 8.9. Derive the differential equations that describe the number of pounds x( and x() of salt at any time in tanks A and B, respectively pure water 3 gal/min mixture I gal/min mixture mixture 3 gal/min 4 gal/min C. Print out and turn in all of your MATLAB code and results. Make sure that your name has been typed into your MATLAB code.

Answer 1

for a galtom A ncomfn - olt SO r a iallon 2 니지 2 2S o0 2J 2기 2 25 プ110)ニ 25

writing in matrix form

$\begin{pmatrix} x_1'\\ x_2' \end{pmatrix} = \begin{pmatrix} -2/25 &1/50 \\ 2/25 & -2/25 \end{pmatrix}\begin{pmatrix} x_1\\ x_2 \end{pmatrix}$

with initial condition given above

%%% Matlab code

clc;
close all;
clear all;
A=[-2/25 1/50;2/25 -2/25];
b=[25 0]';
syms s
B=s*eye(2)-A;
xt=ilaplace(inv(B)*b);

%%%
disp('solution is ');
fprintf('x_1(t)=')
disp(xt(1))
fprintf('x_2(t)=')
disp(xt(2))

OUTPUT:

solution is
x_1(t)=(25*exp(-t/25))/2 + (25*exp(-(3*t)/25))/2

x_2(t)=25*exp(-t/25) - 25*exp(-(3*t)/25)