Solve the following differential equation
Given
This is a first order linear differential equation of the form
Here, and
The integrating factor (I.F) of this differential equation is,
We have
Hence, the solution of the differential equation is,
Let cot–1y = t
[Differentiating both sides]
By substituting this in the above integral, we get
Recall
⇒ xet = –{tet – et} + c
⇒ xet = –tet + et + c
⇒ xet × e–t = (–tet + et + c)e–t
⇒ x = –t + 1 + ce–t
[∵ t = cot–1y]
Thus, the solution of the given differential equation is