Question

Solve:
`1(1/ysinx/y-y/x^(2)cosy/x+1)dx+(1/xcosy/x-x/y^(2)sin y/x+1/y^(2))dy=0`

Answer 1

We have,
`(dx)/y-(xdy)/(y^(2))sinx/y+(dy)/(x)-(ydx)/(x^(2))cosy/x+dx+(dy)/y^(2)=0`
`therefore (ydx-xdy)/(y^(2))sinx/y+(xdy-ydx)/(x^(2))cosy/x+dx+(dy)/(y^(2))=0`
`rArr sinx/y.d(x/y)+cosy/x.d(y/x)+dx+(dy)/y^(2)=0`
Integrating, we get
`-cosx/y+siny/x+x-1/y=C`