input function to ode in matlab

To input a function into Matlab's ODE solvers, you will need to define a function that evaluates the right-hand side of the differential equation. This function should take in two arguments, namely the independent variable t and the dependent variables y, and should return the derivative of each component of y evaluated at t.

The general syntax for defining a function that can be used as an input to Matlab ODE solvers is as follows:

main.m
function dydt = myodefun(t,y)
% define the right-hand side of the differential equation here
dydt = [f1(t,y); f2(t,y); f3(t,y); ...];
end
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where f1, f2, f3, etc. are the functions that define the derivative of each component of y.

Once you have defined this function, you can pass it as an input to Matlab's ODE solvers, such as ode45, which will numerically integrate the differential equation over a specified range of t.

Here is an example of how you can use ode45 to solve a simple first-order differential equation dy/dt = -y:

main.m
% define the right-hand side of the differential equation
function dydt = myodefun(t,y)
dydt = -y;
end

% set the initial condition
y0 = 1;

% set the range of t over which to integrate the differential equation
tspan = [0 10];

% call the ode solver
[T,Y] = ode45(@myodefun, tspan, y0);

% plot the result
plot(T,Y);
xlabel('t');
ylabel('y');
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