Differential Equations Question 84
Question: Solution of $ (xy\cos xy+\sin xy)dx+x^{2}\cos xydy=0 $ is
Options:
A) $ x\sin (xy)=k $
B) $ xy\sin (xy)=k $
C) $ \frac{x}{y}\sin (xy)=k $
D) $ x\sin (xy)=k $
Show Answer
Answer:
Correct Answer: A
Solution:
$ [xy\cos (xy)+\sin (xy)]dx+x^{2}\cos (xy)dy=0 $
$ xy\cos (xy)dx+x^{2}\cos (xy)dy+\sin (xy)dx=0 $
$ x\cos (xy)(ydx+xdy)+\sin (xy)dx=0 $
$ \cot (xy)dxy+\frac{dx}{x}=0 $
$ \log \sin (xy)+\log x=k $
Therefore $ x\sin (xy)=k $ .
BETA
