Differential Equations Question 324
Question: The equation of the curve that passes through the point $ (1,2) $ and satisfies the differential equation $ \frac{dy}{dx}=\frac{-2xy}{(x^{2}+1)} $ is
Options:
A) $ y(x^{2}+1)=4 $
B) $ y(x^{2}+1)+4=0 $
C) $ y(x^{2}-1)=4 $
D) None of these
Show Answer
Answer:
Correct Answer: A
Solution:
$ \frac{dy}{dx}=\frac{-2xy}{(x^{2}+1)} $
Therefore $ \frac{dy}{y}=-\frac{2x}{x^{2}+1}dx $
On integrating, we get $ \log y=-\log (1+x^{2})+\log c $
Therefore $ y(1+x^{2})=c $
Since curve passes through (1, 2), we have $ c=2(1+1^{2}) $
Therefore $ c=4 $
Hence solution is $ y(x^{2}+1)=4 $ .
BETA
