Differential Equations Question 343
Question: The solution of the differential equation $ x^{2}dy=-2xydx $ is
[SCRA 1990]
Options:
A) $ xy^{2}=c $
B) $ x^{2}y^{2}=c $
C) $ x^{2}y=c $
D) $ xy=c $
Show Answer
Answer:
Correct Answer: C
Solution:
$ x^{2}dy=-2xydx $
Therefore $ \frac{1}{y}dy=-\frac{2x}{x^{2}}dx $
On integrating, $ \log y=-2\log x+\log c $
Therefore $ \log y=\log {x^{-2}}+\log c $
Therefore $ \log yx^{2}=\log c $ or $ yx^{2}=c $ .
BETA
