ODE solvers (ode45) in MATLAB - Mini Project: Build & Apply

Solving a Simple ODE with ode45 in MATLAB

📖 Scenario: You want to understand how to solve a simple ordinary differential equation (ODE) using MATLAB's ode45 solver. This is useful in many real-life situations like modeling population growth or cooling of an object.

🎯 Goal: Learn how to set up and solve the ODE dy/dt = -2y using ode45 and plot the solution over time.

📋 What You'll Learn

Create a function for the ODE

Set the time span for the solution

Use ode45 to solve the ODE

Plot the solution with labels

💡 Why This Matters

🌍 Real World

ODE solvers like ode45 are used in engineering, physics, biology, and finance to model how things change over time.

💼 Career

Understanding how to use numerical solvers is important for jobs in data science, engineering, and research where modeling real-world systems is required.

1

Define the ODE function

Create a function handle called odefun that takes inputs t and y and returns -2 * y.

MATLAB

% Define the ODE function handle
% Your code here

Need a hint?

Use the syntax odefun = @(t, y) expression; to create the function handle.

2

Set the time span and initial condition

Create a variable tspan as a vector from 0 to 5, and a variable y0 with the initial value 1.

MATLAB

odefun = @(t, y) -2 * y;
% Define the time span vector 'tspan' and initial value 'y0'
% Your code here

Need a hint?

Use square brackets to create the vector for tspan.

3

Solve the ODE using ode45

Use ode45 with odefun, tspan, and y0 to get outputs t and y.

MATLAB

odefun = @(t, y) -2 * y;
tspan = [0 5];
y0 = 1;
% Solve the ODE with ode45
% Your code here

Need a hint?

Call ode45 with the function handle, time span, and initial value.

4

Plot the solution

Use plot(t, y) to plot the solution. Add xlabel('Time t'), ylabel('Solution y'), and title('Solution of dy/dt = -2y using ode45').

MATLAB

odefun = @(t, y) -2 * y;
tspan = [0 5];
y0 = 1;
[t, y] = ode45(odefun, tspan, y0);
% Plot the solution with labels and title
% Your code here

Need a hint?

Use plot and add labels and title for clarity.