Differential Equations Question 357
Question: The solution of the differential equation $ (1+x^{2})\frac{dy}{dx}=x(1+y^{2}) $ is
[AISSE 1983]
Options:
A) $ 2{{\tan }^{-1}}y=\log (1+x^{2})+c $
B) $ {{\tan }^{-1}}y=\log (1+x^{2})+c $
C) $ 2{{\tan }^{-1}}y+\log (1+x^{2})+c=0 $
D) None of these
Show Answer
Answer:
Correct Answer: A
Solution:
$ (1+x^{2})\frac{dy}{dx}=x(1+y^{2}) $
Therefore $ \frac{1}{1+y^{2}}dy=\frac{x}{1+x^{2}}dx $
On integrating, we get $ {{\tan }^{-1}}y=\frac{1}{2}\log (1+x^{2})+c $
Therefore $ 2{{\tan }^{-1}}y=\log (1+x^{2})+c $ .
BETA
