The degree of a differential equation is the exponent of the highest derivative after the equation has been made polynomial in derivatives. If the equation contains fractional powers or irrational functions of derivatives, it must first be simplified to become polynomial before determining its degree.
Class 12 Maths Chapter 9 on Differential Equations covers the relationship between a function and its derivatives. It introduces methods to solve first-order and higher-order differential equations. The chapter also explores applications like motion population growth and decay. Understanding these concepts is essential for the CBSE Exam 2024-25 and problem-solving.
Share
The given differential equation is as follows:
d/dx ((dy/dx)³)
We will break it down step by step to find the order and degree of the differential equation.
Order: The order of a differential equation is the highest derivative of the unknown function in the equation, which in this case is y.
In the expression d/dx ((dy/dx)³), we differ_intiate the third power of the first derivative, dy/dx. Therefore, the highest order in the expression is the second derivative of y, that is, d²y/dx² .
Thus, the order is 2 .
Degree: The degree of a differential equation is the exponent of the highest-order derivative, provided the equation is polynomial in the derivatives.
Here the highest-order derivative is (dy/dx)² (occurs after differentiation), the degree of the equation is 1 because the expression (dy/dx)³ is raised to the first power (after differentiation).
Hence, the degree is 1.
Sum of the order and degree: The sum of the order and the degree is:
Order + Degree = 2 + 1 = 3
Hence, the answer is 3.
Click here for more:
https://www.tiwariacademy.com/ncert-solutions/class-12/maths/#chapter-9