write ode45 solver in matlab

To use the ode45 solver in MATLAB, you need to define the system of ordinary differential equations (ODEs) and provide the initial conditions.

Here's an example of how to use the ode45 function to solve a simple ODE:

main.m
% Define the ODE
dydt = @(t, y) 2 * t; % Example ODE: dy/dt = 2t

% Define the time span
tspan = [0, 5]; % Solve from t=0 to t=5

% Define the initial condition
y0 = 0; % y(0) = 0

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

% Plot the solution
plot(t, y)
xlabel('Time')
ylabel('y(t)')
title('Solution of dy/dt = 2t')
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In this example, the anonymous function dydt represents the ODE dy/dt = 2t. The tspan variable defines the time interval over which we want to solve the ODE (from 0 to 5 in this case), and y0 is the initial condition (y at t=0). The ode45 function takes these inputs and returns the solution in the form of two vectors, t and y, which represent the time values and the corresponding solutions of the ODE.

You can customize the ODE function, time span, and initial conditions as per your specific problem.