In each of the following differential equation show that it is homogeneous and solve it.
(x² - y²)dx + 2xydy = 0

Question

In each of the following differential equation show that it is homogeneous and solve it. (x 2 - y 2 )dx + 2xydy = 0

Philoid · Accepted Answer

(x² - y²)dx + 2xydy = 0

⇒ the given differential equation is a homogenous equation.

The solution of the given differential equation is :

Put y = vx

Integrating both the sides we get:

Resubstituting the value of y = vx we get

Ans: x² + y² = cx

In each of the following differential equation show that it is homogeneous and solve it.(x2 - y2)dx + 2xydy = 0