solve a system of two odes in matlab

To solve a system of two ordinary differential equations using Matlab, you can follow these steps:

1. Define the system of equations in the form of first-order ODEs. For example, suppose you have the system:

main.m
dx/dt = 2x - 3y
dy/dt = x + 4y
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You can re-write this as:

main.m
dydt = @(t, y) [2*y(1) - 3*y(2); y(1) + 4*y(2)];
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This creates an anonymous function dydt that takes in the current time t and the current values of x and y (stored in the vector y) and returns the derivatives of x and y as a column vector.

2. Choose a solver method. One good choice is the ode45 function, which is a variable-step solver based on the Runge-Kutta method.

3. Call the chosen solver method with the function dydt, and the initial conditions for x and y.

For example, using the system of equations above and initial conditions x(0) = 0 and y(0) = 1, you can solve the system over the time interval [0, 10] with the following code:

main.m
tspan = [0, 10];
y0 = [0; 1];
[t, y] = ode45(dydt, tspan, y0);
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The output t is a vector of time values, and y is a matrix where the first column is the solution for x and the second column is the solution for y.