Differential Equations Question 88
Question: The solution of the differential equation $ xdy+ydx-\sqrt{1-x^{2}y^{2}}dx=0 $ is
Options:
A) $ {{\sin }^{-1}}xy=c-x $
B) $ xy=\sin (x+c) $
C) $ \log (1-x^{2}y^{2})=x+c $
D) $ y=x\sin x+c $
Show Answer
Answer:
Correct Answer: B
Solution:
$ xdy+ydx=\sqrt{1-x^{2}y^{2}}dx $
Therefore $ \frac{xdy+ydx}{\sqrt{1-x^{2}y^{2}}}=dx $
$ \frac{dxy}{\sqrt{1-{{(xy)}^{2}}}}=dx $ . Integrating both side, we get $ {{\sin }^{-1}}xy=x+c $
Therefore $ xy=\sin (x+c) $ .
BETA
