how do i use ode45 in matlab

ode45 in MATLAB is used to solve ordinary differential equations (ODEs) and initial value problems. It is a solver that uses Runge-Kutta method with variable time step for solving the ordinary differential equations of 1st order or 2nd order.

Here is the syntax to use ode45:

[t, y] = ode45(function, tspan, y0)
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Where:

• function is the handle to the function that calculates the derivatives of the system at each time step.
• tspan is a 2-element vector that contains the start and end times for the simulation.
• y0 is a column vector that contains the initial conditions for the system.

For example, let's say you have a differential equation y' = 2*t^2 and the initial condition y(0) = 0. You can define the function that calculates the derivative as:

function dydt = fun(t,y)
dydt = 2*t^2;
end
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Then, you can call ode45 function as:

[t, y] = ode45(@fun, [0 1], 0);
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This will give you the solution y at times t. You can plot the solution using the command plot(t, y).

Note that ode45 requires the initial time t0 to be included in the tspan vector. Also, the output t is a column vector that contains the time points at which the solution is computed, and y is a matrix where columns are corresponding to states function.

Hope this helps!