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Solve: {(xy)cos(xy)+sin(xy)}dx+x^2cos(xy...

Solve: `{(xy)cos(xy)+sin(xy)}dx+x^2cos(xy)dy=0`

A

`x sin (xy)=k`

B

`xy sin(xy)=k`

C

`x/y sin(xy)=k`

D

`x sin(xy)+xy cos xy=k`

Text Solution

Verified by Experts

The correct Answer is:
A
`[xy cos(xy)+sin(xy)]dx+x^(2)cos (xy)dx=0`
`xy cos(xy)dx+x^(2)+cos(xy)dy+dx=0`
`x cos (xy)(ydx+xdy)+sin (xy)dx=0`
`cot (xy)d(xy)+(dx)/(x)=0`
`log sin(xy)+logx=k rArr x sin(xy)=k`
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