A) \[x\sin (xy)=k\]
B) \[xy\sin (xy)=k\]
C) \[\frac{x}{y}\sin (xy)=k\]
D) \[x\sin (xy)=k\]
Correct Answer: A
Solution :
\[[xy\,\cos (xy)+\sin (xy)]dx+{{x}^{2}}\cos (xy)dy=0\] \[xy\,\cos (xy)dx+{{x}^{2}}\cos (xy)dy+\sin (xy)dx=0\] \[x\,\cos (xy)(ydx+xdy)+\sin (xy)dx=0\] \[\cot (xy)dxy+\frac{dx}{x}=0\] \[\log \,\sin (xy)+\log x=k\] Þ \[x\,\sin (xy)=k\].
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