Differential Equations Question 5
Question: An integrating factor of the differential equation $ (1-x^{2})\frac{dy}{dx}-xy=1, $ is
[MP PET 2001]
Options:
A) - x
B) $ -\frac{x}{(1-x^{2})} $
C) $ \sqrt{(1-x^{2})} $
D) $ \frac{1}{2}\log (1-x^{2}) $
Show Answer
Answer:
Correct Answer: C
Solution:
$ (1-x^{2}).\frac{dy}{dx}-xy=1 $
Therefore $ \frac{dy}{dx}-\frac{x}{1-x^{2}}.y=\frac{1}{1-x^{2}} $
I.F. $ ={e^{\int{p.dx}}}={e^{\int{\frac{-x}{1-x^{2}}dx}}} $
$ ={e^{\frac{1}{2}\log (1-x^{2})}}=\sqrt{1-x^{2}} $ .
BETA
