Show that the following differential equation is homogeneous, and then solve it:

Given:

To find: a particular solution of the given differential equation

{∵ λ⁰= 1}

So, F(x, y) is a homogeneous function of degree zero

⇒ It is a homogeneous differential equation

Let y = vx

Differentiating with respect to x:

Integrating both sides:

Let log v – 1 = t

Now, put t = log v – 1:

⇒ log(log v – 1) = log |x| + log v + log c

⇒ log(log v – 1) = log vxc

⇒ log v – 1 = vxc

Put :

Hence, the solution of differential equation is