In each of the question, show that the given differential equation is homogeneous and solve each of them.
(x – y)dy – (x + y)dx = 0
(x - y)dy = (x + y)dx
Here, putting x = kx and y = ky
Therefore, the given differential equation is homogeneous.
(x - y)dy – (x + y)dx = 0
To make it we make the substitution.
y = vx
Differentiating eq. with respect to x, we get
Integrating both sides we get,
2vdv = dt
The required solution of the differential equation.