பொதுமைப்படுத்தப்பட்ட பொய் கோட்பாடு மற்றும் பயன்பாடுகளின் இதழ்

Linear Differential Equations: Definition, Solution Methods and Properties

Abstract

Gustav Sjobeck

This article provides an introduction to linear differential equations, which are equations involving derivatives of an unknown function that can be expressed as a linear combination of the function and its derivatives. After discussing the basic definitions and terminology, the article outlines various methods for solving linear differential equations, including separation of variables, integrating factors and the method of undetermined coefficients. It also covers some important properties of linear differential equations, such as linearity, superposition and the existence and uniqueness theorem. The article concludes by exploring some applications of linear differential equations in physics, engineering and other fields.