Table of Contents
What is a Differential Equation?
A differential equation is an equation that expresses a relationship between the derivatives of two or more functions. Differential equations are used to model a wide variety of physical phenomena, including the motion of fluids and the oscillations of electrical circuits.
Order and Degree of a Differential Equation
A differential equation is an equation that relates a function to its derivatives. In order to solve a differential equation, you must first determine the order and degree of the equation.
The order of a differential equation is the highest derivative that appears in the equation. The degree of a differential equation is the power to which the highest derivative is raised.
For example, the order of the equation y’ = y is 1, and the degree is 1. The order of the equation y” = 2y is 2, and the degree is 2.
Formation of Differential Equations
In mathematics, a differential equation (ODE) is an equation that relates a function with its derivatives. In other words, a differential equation is a mathematical equation that describes how a function changes with respect to another function.
The most common type of differential equation is an equation that relates a function and its derivatives of the first order, also known as a first-order differential equation. First-order differential equations can be solved using mathematical techniques such as integration.
Higher-order differential equations can also be solved, but they are more complicated and require more advanced mathematical techniques.
Differential equations are used in many areas of mathematics, physics, and engineering. They are particularly important in solving problems involving physical systems that change over time, such as fluids flowing through a pipe or vibrations of a guitar string.
