Differential Equations Question 83
Question: The solution of the differential equation, $ ydx+(x+x^{2}y)dy=0 $ is
[AIEEE 2004]
Options:
A) $ \log y=cx $
B) $ -\frac{1}{xy}+\log y=c $
C) $ -\frac{1}{xy}+\log y=c $
D) $ -\frac{1}{xy}+\log y=c $
Show Answer
Answer:
Correct Answer: B
Solution:
$ ydx+xdy=-x^{2}ydy $
Therefore $ \frac{1}{{{(xy)}^{2}}}dxy=-\frac{dy}{y} $
Integrating both side we get $ -\frac{1}{xy}=-\log y+c $
Therefore $ -\frac{1}{xy}+\log y=c $ .
BETA
