A Step-by-Step Guide to Solve First-Order ODEs in MATLAB

In this video, you will learn how to use the ode45 command of MATLAB to solve a first-order ordinary differential equation (ODE). An illustrative example of an one-dimensional first-order ODE is presented to demonstrate the solution. The ode45 is a function that uses a version of the Runge-Kutta method to solve ODEs. The "45" in the function name refers to the fact that the method uses 4th-order and 5th-order accurate steps to solve the ODE. Video Sections: 0:00 Introduction 1:12 Example (one initial condition) 5:25 Example (various initial conditions) %-------- MATLAB CODE ---------% %% Clear and close clc; clear; close all; %% dx/dt = -t^4*x + x, where t = [0,5] and x(0) = 4 % define the function f f = @(t,x)(-t^4*x + x); % tSpan tspan = [0,5]; % x initial condition x0 = 4; % multiple initial condition %x0 = -5:5; % ode45 command [t,x] = ode45(f,tspan,x0); % plot plot(t,x) xlabel('t'); ylabel('x'); #MATLAB #calculus #coding