We have, (tan-1y – x)dy = (1 + y2)dx
It is a linear differential equation of the form
Using: , we get
We have, (i)
Which is a homogeneous differential equation.
Putting y=vx and in (i), we get
Integrating both sides, we get
Substituting , we get
Given that, y=1 when x=0
From (ii), we get
⇒ x2 = 2y2 log|y| is the solution of the given equation.
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