Differential Equations Question 106
Question: The differential equation of the family of curves represented by the equation $ x^{2}y=a $ , is
Options:
A) $ \frac{dy}{dx}+\frac{2y}{x}=0 $
B) $ \frac{dy}{dx}+\frac{2x}{y}=0 $
C) $ \frac{dy}{dx}-\frac{2y}{x}=0 $
D) $ \frac{dy}{dx}-\frac{2x}{y}=0 $
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Answer:
Correct Answer: A
Solution:
$ x^{2}y=a $
(On differentiating) $ x^{2}\frac{dy}{dx}+y\frac{d}{dx}(x^{2})=0 $
Therefore $ x^{2}\frac{dy}{dx}+2xy=0 $
Therefore $ \frac{dy}{dx}+\frac{2y}{x}=0 $ .
BETA
