Differential Equations Question 350
Question: The solution of the differential equation $ \frac{dy}{dx}=\frac{(1+x)y}{(y-1)x} $ is
[AISSE 1986; AI CBSE 1982; MP PET 2004]
Options:
A) $ \log xy+x+y=c $
B) $ \log ( \frac{x}{y} )+x-y=c $
C) $ \log xy+x-y=c $
D) None of these
Show Answer
Answer:
Correct Answer: C
Solution:
$ \frac{dy}{dx}=\frac{(1+x)y}{(y-1)x} $ can be written as $ \frac{y-1}{y}dy=\frac{(1+x)}{x}dx $
Therefore $ ( 1-\frac{1}{y} )dy=( 1+\frac{1}{x} )dx $
Therefore $ (y-\log y)=(x+\log x)+c $
Therefore $ x-y+\log xy=c $ .
BETA
