% 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
