ode 15s in matlab

To use the ode45 function in MATLAB to solve a system of ordinary differential equations, follow these steps:

1. Define your system of differential equations as a function. Let's say we have a system of two differential equations:

main.m
function dydt = myODE(t, y)
    % define your differential equations here
    dydt = zeros(2, 1);
    
    dydt(1) = -2*y(1) + y(2);
    dydt(2) = y(1) - 3*y(2);
end
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2. Set the initial conditions and the time span for the integration:

main.m
y0 = [1; 0];  % initial conditions
tspan = [0 15];  % time span for the integration
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3. Call the ode45 function and pass the function handle for your differential equations, initial conditions, and time span as arguments:

main.m
[t, y] = ode45(@myODE, tspan, y0);
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The output of the ode45 function will be the time points t at which the solution was evaluated and the corresponding solution y to your differential equations.

4. You can now plot the results if desired:

main.m
plot(t, y(:, 1), 'r', t, y(:, 2), 'b');
xlabel('Time');
ylabel('Solution');
legend('y1', 'y2');
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This will plot the solution of y1 in red and the solution of y2 in blue as functions of time.

That's it! You have successfully used ode45 to solve a system of ordinary differential equations in MATLAB.