Differential Equations Question 19
Question: Integrating factor of equation $ (x^{2}+1)\frac{dy}{dx}+2xy=x^{2}-1 $ is
[UPSEAT 2002]
Options:
A) $ x^{2}+1 $
B) $ \frac{2x}{x^{2}+1} $
C) $ \frac{x^{2}-1}{x^{2}+1} $
D) None of these
Show Answer
Answer:
Correct Answer: A
Solution:
$ \frac{dy}{dx}+\frac{2x}{1+x^{2}}y=\frac{x^{2}-1}{x^{2}+1} $
I.F. $ ={e^{\int{\frac{2x}{1+x^{2}}dx}}}={e^{\log (1+x^{2})}} $
$ =1+x^{2} $ .
BETA
