A differential equation is a mathematical equation that relates a function with its derivatives. It describes how a quantity changes over time or space. These equations are classified as ordinary or partial, depending on the number of independent variables, and they are widely used in physics, engineering, and other sciences.
Class 12 Maths Chapter 9 on Differential Equations focuses on understanding the relationship between a function and its derivatives. The chapter introduces methods for solving first order and higher-order differential equations. Applications of differential equations in real-life scenarios such as motion and growth processes are also covered. This chapter is essential for CBSE Exam 2024-25.
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The given differential equation is:
2x dy – y dx = 0
Step 1: Rearrange the equation
Put the equation into the separable variable form as:
(2x dy) = (y dx)
Now dividing both sides by x and changing,
dy/dx = y / (2x)
Step 2: Solution through Separating Variables
Write it,
dy/y = dx/(2x)
Integrating on both sides:
∫ (1/y) dy = ∫ (1/2x) dx
ln|y| = (1/2) ln|x| + C
Step 3: Putting into Exponential Form
Now, taking the exponent on both sides:
y = e^C * x^(1/2)
Let e^C = C’, then:
y = C’ x^(1/2)
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