Solve each of the following initial value problems:
dy = cos x (2 – y cosec x)dx
dy = cos x (2 – y cosec x)dx
Given dy = cos x (2 – y cosec x)dx
This is a first order linear differential equation of the form
Here, P = cot x and Q = 2 cos 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,
Let sin x = t
⇒ cosxdx = dt [Differentiating both sides]
By substituting this in the above integral, we get
Recall
⇒ yt = t2 + c
[∵ t = sin x]
Thus, the solution of the given differential equation is