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Degree Of Differential Equation
Degree of differential equations is the power of the highest derivative in a differential equation. We need to first know the order of the differential equation, to find the degree of the differential equation. The degree of the differential equation is a positive integral value. The degree of the differential equation is similar to the degree of the variable in a polynomial equation.
Let us learn more about the degree of the differential equation, and how to find the degree of the differential equation, with examples, FAQs.
What Is Degree Of Differential Equation?
Degree of the differential equation is the exponent of the highest derivative of the differential equation. The highest derivative of the differential equation is the order of the differential equation, and the power of the highest order of the differential equation is the degree of the differential equation. The degree of a differential equation is always a positive integral value.
Let us first understand that the order of the differential equation can be found by identifying the derivatives in the given expression of the differential equation. The different derivatives in a differential equation are as follows.
 First Derivative: dy/dx or y'
 Second Derivative: d^{2}y/dx^{2}, or y''
 Third Derivative: d^{3}y/dx^{3}, or y'''
 nth derivative: d^{n}y/dx^{n}, or y^{''''.....n times}
Further after identifying the highest derivative in the differential equation, we take the exponent of this highest derivative, to find the degree of the differential equation.The degree of a differential equation is comparable with the degree of the variable in the polynomial expression. Here we will try to find the degree of the following differential equations.
 (a). 4(d^{3}y/dx^{3})  (d^{2}y/dx^{2})^{3 }+ 5(dy/dx) + 4 = 0. Here the differential equation has third derivative as the highest derivative, and the degree of this differential equation is one.
 (b). 7(d^{4}y/dx^{4})^{2} + 5(d^{2}y/dx^{2})^{4}+ 9(dy/dx)^{8} + 11 = 0. Here the differential equation has the fourth derivative as the highest derivative, and the degree of this differential equation is two.
 (c). 3(d^{2}y/dx^{2})^{4} + x(dy/dx)^{2} + y= 0. Here the differential equation has the second derivative as the highest derivative, and the degree of this differential equation is four.
 (d). (y''')^{2 }+ x^{2}(y')^{3}  2x + 11 = 0. Here the differential equation has the third derivative as the highest derivative, and the degree of this differential equation is two.
 (e). (d^{3}y/dx^{3})^{2} + (dy/dx)  Cos^{3}x = 0. Here the differential equation has the third derivative as the highest derivative, and the degree of this differential equation is two.
How To Find Degree Of Differential Equation?
The degree of a differential equation is the exponent of the highest order or the highest derivative in a differential equation. The degree of a differential equation can be computed in two simple steps.
 First Step: As a first step we need to find the order of the differential equation, which is the highest derivative present in the differential equation.
 Second Step: Further we need to find the Degree of the differential equation, which is the power of the highest derivative in the differential equation.
Let us find the degree of few of the differential equations.
 7(d^{4}y/dx^{4})^{3} + 5(d^{2}y/dx^{2})^{4}+ 9(dy/dx)^{8} + 11y = 0. This differential equation is of fourth order and a degree of three.
 (dy/dx)^{2} + (dy/dx)  Cos^{3}x = 0. This differential equation is first order and of second degree.
 (d^{2}y/dx^{2}) + x(dy/dx)^{3} = 0. This differential equation is of second order and the first degree.
Related Topics
The following topics are helpful for a better understanding of the degree of the differential equation.
Examples on Degree Of Differential Equation

Example 1: Find the degree of differential equation (d^{3}y/dx^{3}) + 2(d^{2}y/dx^{2})^{2} + 5dy/dx + 7y = 0.
Solution:
The given differential equation is (d^{3}y/dx^{3}) + 2(d^{2}y/dx^{2})^{2} + 5dy/dx + 7y = 0. This is a differential equation has the first, second, ad third differential of the function y. The highest differential is the third differential, and this differential equation is of order 3.
And the power of the third differential of the equation is equal to one, and hence it is a firstdegree differential equation.
Therefore, the degree of the differential equation is one.

Example 2: Find the order and degree of differential equation (d^{2}y/dx^{2})^{2} 2(dy/dx)^{5} + 4 = 0.
Solution:
The given differential equation is (d^{2}y/dx^{2})^{2} 2(dy/dx)^{5} + 4 = 0. This is a differential equation having first and second differential of the function y. The highest differential is the second differential, and hence it is the differential equation of order two.
And the power of the second differential is also two. Hence the degree of this differential equation is 2.
Therefore the differential equation is of degree two and of order two.
FAQs on Degree Of Differential Equation
What Is The Degree Of Differential Equation?
The degree of the differential equation is the exponent or the power of the highest order of the differential equation. The degree of a differential equation is an integral value and can be found only after finding the order of the differential equation.
How To Find The Degree Of Differential Equation?
The degree of a differential equation can be computed in two simple steps. First, we need to find the order of the differential equation which is the highest derivative that can be found in the differential equation. Second, we need to find the degree of the differential equation, which is the power of the highest derivative of the differential equation.
What Is The Difference Between the Degree Of the Differential Equation And the Order Of the Differential Equation?
The degree of the differential equation can be computed only after knowing the order of the differential equation. The order of the differential equation is the highest derivative present in the differential equation, and the degree of the differential equation is equal to the power or the exponent of the highest order of the differential equation.
What Is The Use Of Degree Of Differential Equation?
The degree of the differential equation is useful to solve the differential equation. The number of solutions, and the number of steps required to solve the differential equation is equal to the degree of the differential equation.The
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