A differential equation is a mathematical expression that relates a function to its derivatives. It describes how a quantity changes with respect to another variable. Differential equations are classified into ordinary and partial types and are used to model real-life phenomena such as motion, growth, and heat distribution.
Class 12 Maths Chapter 9 on Differential Equations explores the relationship between a function and its derivatives. It covers techniques for solving first-order and higher-order differential equations. Applications include modeling motion population growth and other real-world phenomena. This chapter is vital for the CBSE Exam 2024-25 and enhances problem-solving skills.
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Starting with the differential equation:
2x dx − 5y dy = 0
Separate variables:
2x dx = 5y dy
Integrate both sides:
∫ 2x dx = ∫ 5y dy
x² = (5/2)y² + C
Rearrange the equation:
x² − (5/2)y² = C
This represents a family of conic sections. Since the equation is of the form:
(x²) − (constant)·(y²) = C
it represents a family of hyperbolas (for nonzero C).
Thus, the correct answer is a hyperbola.
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