Differential Equations Question 341
Question: If $ \frac{dy}{dx}=\frac{xy+y}{xy+x} $ , then the solution of the differential equation is
[SCRA 1980]
Options:
A) $ y=xe^{x}+c $
B) $ y=e^{x}+c $
C) $ y=Ax{e^{x-y}} $
D) $ y=x+A $
Show Answer
Answer:
Correct Answer: C
Solution:
$ \frac{dy}{dx}=\frac{xy+y}{xy+x} $
Therefore $ ( \frac{1+y}{y} )dy=( \frac{1+x}{x} )dx $
On integrating both sides, we get $ \log y+y=\log x+x+\log A $
Therefore $ \log ( \frac{y}{Ax} )=x-y $
Therefore $ y=Ax{e^{x-y}} $ .
BETA
