Help with complex integration

Hey all! i am trying to integrate this using matlab and to plot S against t. all the values seen are constants except for the term S.

Any help would really be appreciated!

Thanks in advance!

Answer 1

[Shashi Kiran]

Hi @Gan Jun,

I understand that you want to integrate and plot S against t using MATLAB.

The given differential equation is:

Let which rearranges the equation to

Below is the MATLAB code to solve and plot S over time using "ode45" solver:

% Assuming constants(Change accordingly)
q = 1;  V = 1;   S0 = 10; k = 1;   E = 1;   Km = 1;  Ki = 1;  

% Define parameters
a = q/V;
b = k*E/q;

% Define ODE as a function handle
dSdt = @(t, S) a * (S0 - S - (b*S) / (Km + S + Ki*S^2));

% Set time span
tspan = [0 10]; % Adjust as needed
S_initial = 1;  % Initial condition for S

% Solve ODE using ode45
[t, S] = ode45(dSdt, tspan, S_initial);

% Plot the results
figure;
plot(t, S, 'b-', 'LineWidth', 2);
xlabel('Time (t)');
ylabel('S');
title('S vs Time');
grid on;

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Ensure you update the values of based on your data.

For more details on using "ode45", refer to the MATLAB documentation: https://www.mathworks.com/help/matlab/ref/ode45.html

Hope this helps!