Show that the differential equation is homogeneous. Find the particular solution of this differential equation, given that x =1 when

Given differential equation,

….(1)

Clearly, it is a homogeneous differential equation.

Now, let …(2)

…..(3)

Putting (2) and (3) in (1),

Integrating both the sides, we get

Put

For particular solution, put

⇒ C =0

So, the particular solution of given differential equation is=