differential equation in matlab

To solve differential equations in MATLAB, you can use the built-in function ode45. This function can handle both initial value problems and differential algebraic equations. Here's an example of how to use ode45 to solve an initial value problem:

main.m
% Define the differential equation
f = @(t, y) -y + 1;

% Define the initial conditions
y0 = 0;

% Define the time span
tspan = [0, 5];

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

% Plot the solution
plot(t, y);
xlabel('t');
ylabel('y');
title('Solution to y'' = -y + 1');
295 chars
18 lines

In this example, we define the differential equation y' = -y + 1, the initial condition y(0) = 0, and the time span t = [0, 5]. We then use ode45 to solve the differential equation and store the solution in the vectors t and y. Finally, we plot the solution.

For more complex differential equations, you may need to use partial differential equations and/or numerical methods to approximate the solution. MATLAB has many tools for these tasks as well.