Q. 155.0( 1 Vote )

# Find the particular solution of the differential equation

given that when

Answer :

**Given:** (1 – y^{2})(1 + log x)dx + 2xy dy = 0

**To find:** a particular solution of the given differential equation

(1 – y^{2})(1 + log x)dx + 2xy dy = 0

Integrating both sides:

In first integral:

Put 1 + log x = t

In second integral:

Put 1 – y^{2} = 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

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