ode45 example with 3 equations in matlab

main.m
% Define the function for the system of equations
function dydt = myODEs(t, y)
    % Extract variables from the input vector
    x = y(1);
    y = y(2);
    z = y(3);

    % Define the system of equations
    equation1 = x - 2*y + z;
    equation2 = x^2 + y^2 - 9;
    equation3 = 3*x - y - z^2;

    % Return the derivative vector
    dydt = [equation1; equation2; equation3];
end

% Set initial conditions and time span
initialConditions = [0; 0; 0];
timeSpan = [0 10];

% Call the ode45 solver
[t, sol] = ode45(@myODEs, timeSpan, initialConditions);

% Extract the solutions for each variable
xSol = sol(:, 1);
ySol = sol(:, 2);
zSol = sol(:, 3);

% Plot the solutions
plot(t, xSol, 'r', t, ySol, 'g', t, zSol, 'b');
legend('x', 'y', 'z');
xlabel('Time');
ylabel('Solution');
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