First Order Non-Linear Differential Equation

[Nathan W0]

Homework Statement

(x+y)dx-(x-y)dy=0

Homework Equations

The Attempt at a Solution

The solution is c=arctan^-1(y/x)-(1/2)*ln(x^2+y^2) but I don't know how to get the answer. If someone could explain how to solve the above DE, that would be great.

 

[hunt_mat]

The DE is of te form:
$$\frac{dy}{dx}=\frac{x+y}{x-y}$$
Use the following substitution $$y(x)=xv(x)$$ The equation will become solvable.

Mat

 

[Nathan W0]

Oh, Okay I understand it now. Is there any way to know what substitution you would need to use?