Differential Equations Question 81
Question: If $ xdy=y(dx+ydy),y>0 $ and $ y(1)=1, $ then $ y(-3) $ is equal to
[IIT Screening 2005]
Options:
A) 1
B) 3
C) 5
D) -1
Show Answer
Answer:
Correct Answer: B
Solution:
$ xdy=y(dx+ydy) $
Therefore $ \frac{xdy-ydx}{y^{2}}=dy $
Therefore $ -d( \frac{x}{y} )=dy $
Integrating both sides, we get $ \frac{x}{y}+y=c $
$ \because $ $ y(1)=1\Rightarrow c=2 $ ;
$ \therefore $ $ \frac{x}{y}+y=2 $
For $ x=-3 $ , $ y^{2}-2y-3=0\Rightarrow y=-1 $ or 3
$ \Rightarrow y=3 $
$ (\because y>0) $
BETA
