Find the general solution of the differential equations:`x(dx)/(dy)+y-x+x ycotx=0(x!=0)`

Explanation

`x(dy)/(dx)+y-x+xy cot x=0`
`implies (dy)/(dx)+y((1)/(x)+cotx)=1`
Here, `P=(1)/(x)+cotx` and `Q=1`
`:. I.F.=e^(intPdx)=e^(int((1)/(x)+cotx)dx)`
`=e^(logx+logsinx`
`=e^(log(xsinx))=x sin x`
and general solution :
`y*(x sin x)=int1*x sin x dx+c`
`=x(-cosx)-int1*(-cosx)dx+c`
`implies xy sinx=-x cosx+sinx+c`