Degree of Differential Equation
The degree of a differential equation(when it is a polynomial equation in derivatives) is the highest power (positive integral index) of the highest-order derivative involved in the given differential equation.
Example: [Tex](\frac{dy}{dx})^{2} +\frac{d^{2}y}{dx} + 5 = 0 [/Tex]. In this equation highest degree derivative has power of 1. So, the order of differential equation is 1.
Note: It is not always necessary that degree and order of a differential equation are equal, but both of them must be positive.
Differential Equations
Differential Equations come into play in a variety of applications such as Physics, Chemistry, Biology, Economics, etc. A differential equation is a mathematical equation that relates some function with its derivatives. In applications, the functions usually represent physical quantities, the derivatives represent their rates of change, and the equation defines a relationship between the two. Let’s formally define what is a differential equation.
Table of Content
- What is a Differential Equation?
- Order of a Differential Equation
- Degree of Differential Equation
- Types of Differential Equations
- General And Particular Solution of Differential Equation
- Formation of a Differential Equation whose General Solution is Given
- Homogeneous Differential Equations
- Variable Separable Differential Equation
- Solution to a Linear Differential Equation
- Writing a Differential Equation
- Differential Equations Class 12