Table of Contents
Linear Differential Equations Definition
A linear differential equation is defined by the linear polynomial equation, which consists of derivatives of several variables. It is also stated as Linear Partial Differential Equation when the function is dependent on variables and derivatives are partial.
A differential equation having the above form is known as the first-order linear differential equation where P and Q are either constants or functions of the independent variable (in this case x) only.
Also, the differential equation of the form, dy/dx + Py = Q, is a first-order linear differential equation where P and Q are either constants or functions of y (independent variable) only.
To find linear differential equations solution, we have to derive the general form or representation of the solution.
Non-Linear Differential Equation
A non-linear differential equation is a differential equation in which the coefficients of the different terms are not all constant. This makes the equation difficult to solve, as the solution depends on the path taken through the equation. Non-linear differential equations are often used to model physical phenomena, which can be unpredictable and non-linear in nature.
