How to solve and plot a differential equation

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AUSTIN WHITELEY
AUSTIN WHITELEY 2022-1-18
回答： Vandit 2023-6-28
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.

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回答（1 个）

Vandit
Vandit 2023-6-28
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

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