The solution of the differential equation

(1 + y²)dx = (tan^-1 y - x)dy is

Concept:

The standard form of a first-order linear differential equation is,

Form 1: 

Where P and Q are the functions of x.

Integrating factor, 

Now, the solution for the above differential equation is,

Form 2: 

Where P and Q are the functions of y.

Integrating factor, 

Now, the solution for the above differential equation is,

Calculation:

The given differential equation is,

(1 + y²) dx = (tan^-1 y - x) dy

Now, it is in the standard form of a first-order linear differential equation.

Here, 

Integrating factor:

Now, the solution of the given differential equation is

Let 

Now, the solution becomes