How to solve and plot a differential equation

Use Matlab to solve for the matrix 𝑴 and the vector 𝐹⃗ . Plot the concentration in each compartment vs. time. dC/dt + 𝑀𝐶⃗ = 𝐹⃗

C= [c1; c2]

when dC/dt=0, c1=.8333 c2=2.08333.

Here's what I have in terms of code

C=[c1; c2];

M= [1.5 -.12; -1 .4];

F=[1; 0];

syms c(t)

ode= diff (c,t) + M*C == F

sol=dsolve(ode)

fplot(sol,[0,5]);

It is having trouble with the fact that C is a vector with two other variables.

[James Tursa]

You have numeric values for M and F?

[AUSTIN WHITELEY]

yes.

M= [1.5 -.12; -1 .4];

F=[1; 0];

Answer 1

[Vandit]

Hi,

Below is the updated MATLAB code that solves the given differential equation and plot the concentration in each compartment over time :

M = [1.5 -0.12; -1 0.4];
F = [1; 0];
c1=.8333
c2=2.08333;
C0 = [c1; c2];
tspan = [0 10]; % Adjust the time span as needed

% Solve the differential equation
[t, C] = ode45(@(t, C) M*C + F, tspan, C0);

% Plot the concentration in each compartment vs. time
figure;
plot(t, C(:, 1), 'b', 'LineWidth', 2); % Compartment 1
hold on;
plot(t, C(:, 2), 'r', 'LineWidth', 2); % Compartment 2
xlabel('Time');
ylabel('Concentration');
legend('Compartment 1', 'Compartment 2');
title('Concentration vs. Time');
grid on;

I have also attached the output plot which should be obtained after running the above code in MATLAB.

To know more about the Ordinary Differential Equations refer to the link below:

Ordinary Differential Equations - MATLAB & Simulink (mathworks.com)

Hope this helps.

Thankyou