use ode45 for 11 differential equations in matlab

To use the ode45 function in MATLAB to solve a system of 11 differential equations, you need to follow these steps:

1. Define a function file that represents your system of differential equations. Let's say you name this file odeFunc.m.

2. In the function file, define the differential equations as a function of the dependent variables (y) and the independent variable (t). The function should take two input arguments: t and y, and return a column vector of the derivatives dy/dt. The size of the output vector should match the size of the input vector y. For example, if your system of equations is:

   dy1/dt = f1(t, y1, y2, ..., y11) dy2/dt = f2(t, y1, y2, ..., y11) ... dy11/dt = f11(t, y1, y2, ..., y11)

   Then your odeFunc.m file should look like this:

   main.m
   function dydt = odeFunc(t, y)
       % extract the dependent variables from the input vector y
       y1 = y(1);
       y2 = y(2);
       ...
       y11 = y(11);
   
       % define the differential equations
       dy1dt = f1(t, y1, y2, ..., y11);
       dy2dt = f2(t, y1, y2, ..., y11);
       ...
       dy11dt = f11(t, y1, y2, ..., y11);
   
       % return the derivatives as a column vector
       dydt = [dy1dt; dy2dt; ...; dy11dt];
   end
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3. Now, in your main MATLAB script or command window, you can call the ode45 function to solve the system of differential equations. The syntax for ode45 is:

   main.m
   [t, y] = ode45(@odeFunc, tspan, y0)
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   where @odeFunc is the function handle to your odeFunc.m file, tspan is the time interval over which you want to solve the equations, and y0 is the initial condition vector for the dependent variables.

   For example, if you want to solve the system of differential equations from t = 0 to t = 10 with an initial condition vector y0, your code would look like this:

   main.m
   tspan = [0, 10];  % time interval
   
   % initial condition vector
   y0 = [y1_0; y2_0; ... ; y11_0];
   
   % solving the system of differential equations
   [t, y] = ode45(@odeFunc, tspan, y0);
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   After running the code, the t variable will contain the time values at which the solution was computed, and y will be a matrix where each column corresponds to the values of the dependent variables at each time point.

Make sure to replace f1, f2, ..., f11 with the actual functions that define your differential equations, and y1_0, y2_0, ..., y11_0 with the initial values for your dependent variables.

Note: It's important to ensure that the dimensions of your input arguments and output vector are consistent. Also, make sure that the dimension of y0 matches the number of dependent variables in your system of equations.