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Assertion (A) : The differential equation of the family of rectangular hyperbolas which have the coordinate axes as asymptotes is ${xy}_{1} + y = 0$
Reason (R) : The number of arbitrary constants in the general solution of differential equation is equal to the order of the differential equation.
Then the Statement among the following is

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(A) false (R) is true

(A) is true, (R) is false

Both (A) and (R) are true and R is correct explanation of A

Both (A) and (R) are true and R is not correct explanation of A

answer is A.

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Detailed Solution

$xy = c^{2}$

D.w.r.t y

$x \frac{dy}{dx} + y = 0 [\frac{dy}{dx} = y_{1}] \Rightarrow xy + y = 0$

order = highest derivation

Order = 1

$∴$ Both (A) and (B) are true and R is correct explanation of A

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