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

Options

A. `x sin (xy)=k`
B. `xy sin(xy)=k`
C. `x/y sin(xy)=k`
D. `x sin(xy)+xy cos xy=k`

Answer

A

Explanation

`[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`