A differential equation is a mathematical equation that relates a function to its derivatives. It describes how a quantity changes with respect to another variable. These equations can be classified as ordinary or partial and are widely used in fields such as physics engineering biology and economics.
Class 12 Maths Chapter 9 on Differential Equations focuses on the relationship between a function and its derivatives. It includes methods to solve first-order and higher-order differential equations. Real-world applications such as motion population growth and decay are discussed. This chapter is essential for the CBSE Exam 2024-25 and practical problem-solving.
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The differential equation given is:
sin(x) + cos(dy/dx) = y²
To know the degree of the differential equation, we have the following steps:
1. Rearrange the formula: The formula contains dy/dx that is not raised to any power directly. However, with the term cos(dy/dx) the degree calculation is complicated since it deals with a trigonometric function of the derivative.
2. Degree of a differential equation: The degree of a differential equation is defined to be the highest power of the highest-order derivative after the equation has been made free from any irrational terms, fractional powers, or trigonometric functions involving derivatives.
3. This equation contains a trigonometric function, cos(dy/dx), whose argument is a first derivative, not an algebraic expression, not a polynomial, not a simple rational term. Since it’s placed within the argument of a trigonometric function, the degree is undefined.
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