Hi
Here's a revised version of the code with corrections and proper MATLAB syntax for solving and plotting the solutions to the system of differential equations:
clc;
clear all;
% Define symbolic variables and functions
syms XS(t) X1(t) Y(t)
% Define the differential equations
ode1 = diff(XS, t) == (XS-XS*XS)*(XS-0.17) - (0.36*XS*X1*(theta*0.0001*sqrt(XS)*Y))/(1+0.2*sqrt(XS));
ode2 = diff(X1, t) == (X1)*(0.06*XS - 4.06*X1*Y - 0.09);
ode3 = diff(Y, t) == (0.000089*sqrt(XS)*Y)/(1+0.2*sqrt(XS)) - 0.232*X1 - Y;
% Combine the ODEs into a system
odes = [ode1; ode2; ode3];
% Define initial conditions (example initial conditions, adjust as necessary)
cond1 = XS(0) == 1; % Initial condition for XS
cond2 = X1(0) == 1; % Initial condition for X1
cond3 = Y(0) == 1; % Initial condition for Y
% Solve the system of ODEs
conds = [cond1; cond2; cond3];
[XSSol(t), X1Sol(t), YSol(t)] = dsolve(odes, conds);
% Plot the solutions
fplot(XSSol, 'b', 'LineWidth', 1.5); % Plot XS solution in blue
hold on;
fplot(X1Sol, 'r', 'LineWidth', 1.5); % Plot X1 solution in red
fplot(YSol, 'g', 'LineWidth', 1.5); % Plot Y solution in green
hold off;
% Add legend
legend('XS(t)', 'X1(t)', 'Y(t)');
% Label the axes
xlabel('Time t');
ylabel('Solutions');
% Add a title
title('Solutions to the Differential Equations');
Since it is unclear what the value of ‘theta’ should be, you'll need to assign it a numeric value before using it in the equations. If ‘theta’ is not meant to be a variable from any of the toolboxes like Sensor Fusion and Tracking Toolbox, Navigation Toolbox ,Robotics System Toolbox, ROS Toolbox, UAV Toolbox then simply define it as a constant in your workspace.
For more information refer following documentation:
