Find one-parameter families of solution curves of the following differential equations:
Given
This is a first order linear differential equation of the form
Here, P = cos x and Q = esin x cos x
The integrating factor (I.F) of this differential equation is,
We have
∴ I.F = esin 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
[∵ t = sin x]
Thus, the solution of the given differential equation is