Question
Show that the given differential equation is homogeneous and solve it:
(x-y) dy - (x+y) dx = 0
Solution
The given differential equation is
(x-y) dy - (x+y) dx = 0 or (x-y) dy = (x+y) dy
or
...(1)
It is a differential equation of the form
Here,
Replacing x by
and y by 
(x-y) dy - (x+y) dx = 0 or (x-y) dy = (x+y) dy
or
...(1)It is a differential equation of the form
Here,
Replacing x by
and y by ∴ F(x, y) is a homogeneous function of degree zero.
∴ given differential equation is a homogeneous differential equation.
Put y = v x so that 
Separating the variables, 
Integrating , 
or 
or 
or 
