Differential Equations Question 335
Question: The solution of the differential equation $ (x^{2}-yx^{2})\frac{dy}{dx}+y^{2}+xy^{2}=0 $ is
[Pb. CET 2003]
Options:
A) $ \log ( \frac{x}{y} )=\frac{1}{x}+\frac{1}{y}+c $
B) $ \log ( \frac{y}{x} )=\frac{1}{x}+\frac{1}{y}+c $
C) $ \log ( xy )=\frac{1}{x}+\frac{1}{y}+c $
D) $ \log ( xy )+\frac{1}{x}+\frac{1}{y}=c $
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Answer:
Correct Answer: A
Solution:
The given equation $ (x^{2}-yx^{2})\frac{dy}{dx}+y^{2}+xy^{2}=0 $
Therefore $ \frac{1-y}{y^{2}}dy+\frac{1+x}{x^{2}}dx=0 $
Therefore $ ( \frac{1}{y^{2}}-\frac{1}{y} )dy+( \frac{1}{x^{2}}+\frac{1}{x} )dx=0 $
On integrating, we get the required solution $ \log ( \frac{x}{y} )=\frac{1}{x}+\frac{1}{y}+c $ .
BETA
