Q. 415.0( 1 Vote )

# Find the particular solution of the differential equation y ≠ 0 given that x = 0 when

Given

This is a first order linear differential equation of the form

Here, P = cot y and Q = 2y + y2cot y

The integrating factor (I.F) of this differential equation is,

We have

I.F = sin y [ elog x = x]

Hence, the solution of the differential equation is,

Recall

x sin y = y2 sin y + c

x = y2 + c cosec y

However, when, we have x = 0.

By substituting the value of c in the equation for x, we get

Thus, the solution of the given differential equation is

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