| [Note : C denotes constant of integration] |
A) \[2\cos (xy)+\frac{1}{{{x}^{2}}}=C\]
B) \[2\cos (xy)+{{y}^{2}}=C\]
C) \[2\sin (y)+{{x}^{-2}}=C\]
D) \[2\sin (x\,y)+{{y}^{-2}}=C\]
Correct Answer: A
Solution :
\[{{x}^{4}}dy+{{x}^{3}}ydx+\cos ec\,(xy)\,dx=0\] \[{{x}^{3}}(xdy+ydx)+\cos ec\,(xy)\,dx=0\] \[\therefore \,\,\int_{{}}^{{}}{\frac{d(xy)}{\cos ec\,(xy)}\,+\int_{{}}^{{}}{\frac{dx}{{{x}^{3}}}=0}}\] \[\Rightarrow \,-\cos \,(xy)\,+\frac{{{x}^{-3+1}}}{-3+1}=C\] \[\therefore \,\,2\cos (xy)+{{x}^{-2}}=C\]
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