Find the particular solution of the differential equation

given that when

Given: (1 – y²)(1 + log x)dx + 2xy dy = 0

To find: a particular solution of the given differential equation

(1 – y²)(1 + log x)dx + 2xy dy = 0

Integrating both sides:

In first integral:

Put 1 + log x = t

In second integral:

Put 1 – y² = u

⇒ 2y dy = du

So,

It is given that when x = 1 the value of y = 0

Therefore,

{∵ log 1 = 0}

So, the solution of the differential equation is