solve a differential equation in matlab

To solve a differential equation in MATLAB, you can use several numerical methods available. One commonly used method is the ode45 function, which uses a Runge-Kutta algorithm of order 5 to approximate the solution of the differential equation.

Here's an example of how to use the ode45 function to solve a differential equation:

main.m
% Define the differential equation as an anonymous function
dydt = @(t,y) sin(t);

% Define the initial conditions
t0 = 0;
y0 = 0;

% Define the time span for the solution
tspan = [0 10];

% Solve the differential equation using ode45
[t, y] = ode45(dydt, tspan, y0);

% Plot the solution
plot(t,y)
xlabel('Time')
ylabel('y(t)')
title('Solution of dy/dt = sin(t)')
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In this example, we define the differential equation as an anonymous function, set the initial conditions and time span for the solution, and then use the ode45 function to obtain the solution at different time points. Finally, we plot the solution using the plot function.

Note that ode45 can be used to solve more complex differential equations as well, including systems of differential equations. You can find more information on the ode45 function and other numerical methods for solving differential equations in MATLAB's documentation.