The general solution of rhe differential equation ydx -xdy = 0; (Given x, y > 0), is of the form
The general solution of a differential equation is the most general form of its solution containing arbitrary constants. It includes all possible solutions to the equation. The general solution represents a family of curves or functions that satisfy the given differential equation and is obtained after solving the equation.
Class 12 Maths Chapter 9 on Differential Equations deals with understanding the relationship between a function and its derivatives. It covers techniques for solving first-order and higher-order differential equations. The chapter explores practical applications such as motion and population growth. Mastery of this chapter is crucial for the CBSE Exam 2024-25.
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The given differential equation is:
y dx – x dy = 0
This is a first-order linear differential equation. We can rewrite it as:
y dx = x dy
Now, divide both sides by x and y:
(dx/x) = (dy/y)
This is a separable differential equation, meaning we can integrate both sides separately.
Integrating both sides:
∫(1/x) dx = ∫(1/y) dy
The integrals of 1/x and 1/y are:
ln|x| = ln|y| + C
Now, take both sides as exponents to get rid of the logarithms:
x = C y
Therefore, the general solution is:
y = cx
where c is a constant.
So, the right answer is y = cx.
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