How can the constant C absorb all that other stuff?


This concept comes up in different kinds of problems, but one of the most common is with separable differential equations. Once you've separated variables and integrated both sides of the equation, you have to try to solve for y and simplify the equation at the same time. 

In order to simplify, you'll need to be comfortable combining constants. When you have a constant C, anything that gets directly attached to it can be absorbed into the constant. Like another constant, raising the constant to the base e, or putting a +/- sign in front of the constant. All of these can be rolled into the constant, which significantly simplifies the equation.

Want to learn more about Differential Equations? I have a step-by-step course for that. 😃