Solve the differential equation (1+ y²) tan^-1x dx + 2y (1 + x²) dy = 0

given: (1+y²) tan^-1x dx + 2y(1+x²) dy=0

To find: solution of given differential equation

Re-writing the equation as

Integrating both sides

For LHS

Assume tan^-1 = t

Formula:

For RHS

Assume 1+y²=z

2y dy=dz

Now substituting and integrating both sides

Formula:

Substituting for t and z

Is the solution for the given differential equation