How to determine the general solution to a differential equation

The video tutorial covers the process of factoring and multiplying by DX on both sides of an equation. It then delves into antidifferentiation, focusing on recognizing patterns involving trigonometric functions like tan inverse. The tutorial concludes with solving for Y by applying tangent functions, emphasizing the importance of pattern recognition in mathematical problem-solving.

What does the expression 1 / (1 + y^2) dy equal to in terms of X?

What is the significance of recognizing patterns in integration as mentioned in the text?