Question:
The solution of the differential equation xdy + ydx = 0 is:
The solution of the differential equation xdy + ydx = 0 is:
Updated On: Jul 7, 2022
- xy = c
- $x^2 + y^2 = c$
- xy log x = 1
- log xy = c
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The Correct Option is A
Solution and Explanation
Given, xdy + ydx = 0
Divide both sides above equation by xy,
We get, $\frac{dx}{dy} + \frac{dy}{y} = 0 $
Integrating it on both sides, we get
log x + log y = log c
$\Rightarrow $ log xy = log c $\Rightarrow $ xy = c.
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Concepts Used:
Differential Equations
A differential equation is an equation that contains one or more functions with its derivatives. The derivatives of the function define the rate of change of a function at a point. It is mainly used in fields such as physics, engineering, biology and so on.
Orders of a Differential Equation
First Order Differential Equation
The first-order differential equation has a degree equal to 1. All the linear equations in the form of derivatives are in the first order. It has only the first derivative such as dy/dx, where x and y are the two variables and is represented as: dy/dx = f(x, y) = y’
Second-Order Differential Equation
The equation which includes second-order derivative is the second-order differential equation. It is represented as; d/dx(dy/dx) = d2y/dx2 = f”(x) = y”.
Types of Differential Equations
Differential equations can be divided into several types namely
- Ordinary Differential Equations
- Partial Differential Equations
- Linear Differential Equations
- Nonlinear differential equations
- Homogeneous Differential Equations
- Nonhomogeneous Differential Equations