Linear Differential Equations, Nonlinear Differential Equations

In this article, we explore how to solve various types of equations using MATLAB, including but not limited to linear differential equations and nonlinear differential equations. We discuss different MATLAB tools and techniques, along with solution methods and strategies for various equation types. The article introduces MATLAB's advanced features such as symbolic computation using the Symbolic Math Toolbox (e.g., dsolve function for analytical solutions) and optimization algorithms (e.g., ode45 solver for numerical integration of ODEs). We will demonstrate implementation approaches including defining equation systems, setting initial/boundary conditions, and selecting appropriate solvers based on equation characteristics (stiff vs non-stiff systems). These features help create more accurate and efficient solutions, with practical code examples showing how to handle both ordinary differential equations (ODEs) and differential-algebraic equations (DAEs) through functions like ode15s for stiff problems and pdepe for partial differential equations.