Solve the following differential equation: (1 + y²)dx = (tan–¹y – x)dy

Given Differential equation:

(1 + y²)dx = (tan–¹y – x)dy

Rearranging the terms,

Now this differential equation is linear in x,

Here equation is not homogenous, thus variable separable method will not work.

Integrating factor,

The general solution for the differential equation,

Put t = tan^–1y

This can be solved by using by part integration

I= te^t – e^t

I= e^t (t – 1)

Therefore general solution for the differential equation is

Put t =tan^–1y