Differential Equations Question 92
Question: If c is any arbitrary constant, then the general solution of the differential equation $ ydx-xdy=xydx $ is given by
[J & K 2005]
Options:
A) $ y=cx{e^{-x}} $
B) $ x=cy{e^{-x}} $
C) $ y+e^{x}=cx $
D) $ ye^{x}=cx $
Show Answer
Answer:
Correct Answer: D
Solution:
Given $ ydx-xdy=xydx $
Therefore $ \frac{ydx-xdy}{xy}=dx $
Therefore $ d[ \ln ( \frac{x}{y} ) ]=dx $
Integrating both sides, we get $ \ln \frac{x}{y}+\ln c=x $
Therefore $ ye^{x}=cx $ .
BETA
