i have given three differential equations for which i need graph using matlab code . is the code right?

clc
clear all;
syms XS X1
ode1 = diff(XS) == (XS-XS.*XS)(XS-0.17)−(0.36*XS*X1)(θ.0001*√XS*Y)/(1+0.2*√XS);
ode2 = diff(X1) == (X1)(0.06*XS-4.06*X1*Y-0.09)
ode3 = diff(Y) == (0.000089√XS*Y)/(1+0.2*√XS)-0.232X1-Y
cond = x(s) > 0;
[XSSol(t),X1Sol(t),YSol(t)] = dsolve(odes,conds)
fplot(XSSol)
hold on
fplot(X1Sol)
hold on
fplot(YSol)
legend('XSSol','X1Sol','YSol')

I have written this code and I want to know if the code is right for the given two equations.

Answer 1

[Riya]

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:

https://www.mathworks.com/help/robotics/