The order and degree of the differential equation d²y/dx² + (dy/dx)¹/⁴ + x¹/⁵ = 0 are respectively
In Class 12 Maths, the order of a differential equation refers to the highest derivative present, while the degree is the exponent of the highest derivative, provided the equation is polynomial in derivatives. These concepts help classify and solve differential equations in both theoretical and practical applications.
Class 12 Maths Chapter 9 on Differential Equations deals with the relationship between a function and its derivatives. It covers methods to solve first order and higher-order differential equations. Applications of differential equations in real-world problems such as motion and population growth are explored. This chapter is crucial for CBSE Exam 2024-25.
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The differential equation given is:
d²y/dx² + (dy/dx)^(1/4) + x^(1/5) = 0
Order: The order of a differential equation is the highest derivative of the unknown function, which, in this case, is y.
The highest derivative of the given equation is d²y/dx², the second derivative of y with respect to x. So, 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.
To find the degree, we remove the fractional exponent in the term (dy/dx)^(1/4). We will multiply both sides of the equation by 4 to remove the fractional power. The equation becomes a polynomial in derivatives after that, and the highest derivative is d²y/dx², which has an exponent of 2.
Therefore, the degree is 4.
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