MATLAB Differential Equation Solving Examples

In this example, we will demonstrate how to use MATLAB to solve differential equations. Differential equations are fundamental in scientific and engineering applications, making proficiency in their solution highly valuable. We will begin with a simple first-order differential equation and progressively advance to higher-order equations. The implementation will utilize MATLAB's ode45 solver for non-stiff problems, which employs a Runge-Kutta method with adaptive step-size control. We will also explore alternative solvers like ode15s for stiff systems and demonstrate how to visualize solutions using plotting functions. Through this tutorial, you will learn to define differential equations using function handles, set initial conditions with ode45's syntax [t,y] = ode45(odefun,tspan,y0), and analyze results through graphical representations. This practical approach will equip you with skills to apply MATLAB's differential equation solving capabilities to real-world problems.