Question:
The differential equation of the rectangular hyperbola hyperbola, where axes are the asymptotes of the hyperbola, is
The differential equation of the rectangular hyperbola hyperbola, where axes are the asymptotes of the hyperbola, is
Updated On: Apr 13, 2023
- $y \frac{dy}{dx} = x $
- $x \frac{dy}{dx} = - y $
- $x \frac{dy}{dx} = y $
- $ xdy + ydx = c $
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The Correct Option is B
Solution and Explanation
The differential equation of the rectangular hyperbola $xy = c^2$ is
$ y + x \frac{dy}{dx} = 0 $
$\Rightarrow x \frac{dy}{dx} = - y $
$ y + x \frac{dy}{dx} = 0 $
$\Rightarrow x \frac{dy}{dx} = - y $
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Concepts Used:
General Solutions to Differential Equations
A relation between involved variables, which satisfy the given differential equation is called its solution. The solution which contains as many arbitrary constants as the order of the differential equation is called the general solution and the solution free from arbitrary constants is called particular solution.
For example,
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