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

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Kanwal Aftab el 25 de En. de 2022
Respondida: Riya el 5 de Feb. de 2024
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) == (0.000089XS*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.
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### Respuestas (1)

Riya el 5 de Feb. de 2024
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;
legend('XS(t)', 'X1(t)', 'Y(t)');
% Label the axes
xlabel('Time t');
ylabel('Solutions');
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.
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