Given \((cot^{-1}y+x)dy=(1 + y^2)dx\)
This is a first order linear differential equation of the form
The integrating factor (I.F) of this differential equation is,
Hence, the solution of the differential equation is,
By substituting this in the above integral, we get
Thus, the solution of the given differential equation is \(x=-cot^{-1}y + 1 + ce^{-cot^{-1}y}\)