In each of the following differential equation show that it is homogeneous and solve it.

Question

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

Philoid · Accepted Answer

(x + y)dy + (y - 2x)dx = 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

⇒ y² + 2xy - 2x² = c

Ans: y² + 2xy - 2x² = c