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