Solve each of the following initial value problems:
,
,
Given and
This is a first order linear differential equation of the form
Here, P = cot x and Q = 4x cosec x
The integrating factor (I.F) of this differential equation is,
We have
∴ I.F = sin x [∵ elog x = x]
Hence, the solution of the differential equation is,
Recall
⇒ y sin x = 2x2 + c
∴ y = (2x2 + c) cosec x
However, when, we have y = 0
By substituting the value of c in the equation for y, we get
Thus, the solution of the given initial value problem is