Solve each of the following initial value problems:
, tan x ≠ 0 given that y = 0 when
, tan x ≠ 0 given that y = 0 when
Given and
This is a first order linear differential equation of the form
Here, P = cot x and Q = 2x + x2 cot 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 = x2sin x + c
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