If any differentisl equation in the form
`f(f_(1)(x,y)d(f_(1)(x,y)+phi(f_(2)(x,y)d(f_(2)(x,y))+....=0`
then each term can be intergrated separately.
For example,
`intsinxyd(xy)+int((x)/(y))d((x)/(y))=-cos xy+(1)/(2)((x)/(y))^(2)+C`
The solution of the differential equation
`xdy-ydx=sqrt(x^(2)-y^(2))dx` is

Options

A. `x+sqrt(x^2+y^2)=cx^2`
B. `y-sqrt(x^2+y^2) =cx `
C. `x-sqrt(x^2+y^2)=cx`
D. `y+sqrt(x^2+y^2)=cx^2`

Answer

D