ode 45 in matlab

To use the ode45 function in MATLAB, follow these steps:

1. Define the differential equation that you want to solve.

   main.m
   function dydt = my_ode(t, y)
       dydt = cos(t);
   end
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2. Define the initial condition.

   main.m
   y0 = 0;
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3. Set up the time span for your solution.

   main.m
   tspan = [0 10];
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4. Call the ode45 function and pass in the differential equation (my_ode), initial condition (y0), and time span (tspan).

   main.m
   [t, y] = ode45(@my_ode, tspan, y0);
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5. Plot the solution.

   main.m
   plot(t, y);
   xlabel('Time');
   ylabel('y(t)');
   title('Solution of my ODE');
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This will solve the differential equation dy/dt = cos(t) for t between 0 and 10 with an initial condition of y(0) = 0. The resulting solution y(t) will be plotted as a function of time.