# 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

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