Solve the differential equation

Question:

Solve the differential equation (1 + y2) tan–1x dx + 2(1 + x2dy = 0.

Solution:

Given differential equation, (1 + y2) tan–1x dx + 2(1 + x2dy = 0

2y (1 + x2) dy = -(1 + y2) tan-1x dx

Thus, the above equation is the required solution.