Differential Equations Question 116
Question: The differential equation of the family of curves $ y^{2}=4a(x+a) $ , where a is an arbitrary constant, is
Options:
A) $ y[ 1+{{( \frac{dy}{dx} )}^{2}} ]=2x\frac{dy}{dx} $
B) $ y[ 1-{{( \frac{dy}{dx} )}^{2}} ]=2x\frac{dy}{dx} $
C) $ \frac{d^{2}y}{dx^{2}}+2\frac{dy}{dx}=0 $
D) $ {{( \frac{dy}{dx} )}^{3}}+3\frac{dy}{dx}+y=0 $
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Answer:
Correct Answer: B
Solution:
Given $ y^{2}=4a(x+a) $ . Differentiating, $ 2y( \frac{dy}{dx} )=4a $
Eliminating a from (i) and (ii), required equation is $ y[ 1-{{( \frac{dy}{dx} )}^{2}} ]=2x\frac{dy}{dx} $ .
BETA
