# How do I construct matrices of multiple variables and plot a graph

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Alfred on 23 Jul 2024
Commented: Alfred on 25 Jul 2024
I am a beginner to MATLAB.
I tried but I'm getting errors.
Anybody, kindly help. Thank you.
Equations dx/dt=-2x
dy/dt=2x
Initial condition: x(t=0)=100
y(t=0)=0
tspan=[0 3];
x0=100;
y0=0;
dzdt = (dxdt dydt);
Invalid expression. Check for missing multiplication operator, missing or unbalanced delimiters, or other syntax error. To construct matrices, use brackets instead of parentheses.
[tSol, zSol]=ode45(@odefun,tspan,x0);
plot(tSol, zSol);
function dzdt=odefun(t,z)
x = z(1);
y = z(2);
dxdt = -2*x;
dydt = 2*x;
dzdt = [dxdt;dydt];
end

Hassaan on 23 Jul 2024
% Define the time span and initial conditions
tspan = [0 3];
z0 = [100; 0]; % Initial conditions for x and y, combined into a single column vector
% Call the ODE solver
[tSol, zSol] = ode45(@odefun, tspan, z0);
% Plot the solutions for x and y over time
figure; % Open a new figure window
hold on; % Keep the plot for adding both x and y
plot(tSol, zSol(:,1), 'b-', 'LineWidth', 2); % Plot x with a thicker blue line
plot(tSol, zSol(:,2), 'r--', 'LineWidth', 2); % Plot y with a thicker red dashed line
xlabel('Time t', 'FontSize', 12, 'FontWeight', 'bold');
ylabel('Solutions x and y', 'FontSize', 12, 'FontWeight', 'bold');
title('Solutions to the differential equations dx/dt = -2x and dy/dt = 2x', 'FontSize', 14, 'FontWeight', 'bold');
legend('x(t)', 'y(t)');
grid on; % Turn on grid
set(gca, 'FontSize', 10); % Set the font size for axes
hold off; % Release the plot hold
% Define the system of differential equations
function dzdt = odefun(t, z)
x = z(1);
y = z(2);
dxdt = -2 * x;
dydt = 2 * x;
dzdt = [dxdt; dydt];
end
Torsten on 24 Jul 2024
zSol has two columns: the first is x over time, the second is y over time.
Alfred on 25 Jul 2024
okay. Thank you

Torsten on 23 Jul 2024
tspan=[0 3];
x0=100;
y0=0;
z0=[x0;y0];
[tSol, zSol]=ode45(@odefun,tspan,z0);
plot(tSol, zSol);
function dzdt=odefun(t,z)
x = z(1);
y = z(2);
dxdt = -2*x;
dydt = 2*x;
dzdt = [dxdt;dydt];
end
Alfred on 23 Jul 2024

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