I've termed this section as Intervals of Validity since all of the illustrations will involve them. Though, there is many more to this section. We will notice a couple of theorems which will tell us as we can solve a differential equation. We will also notice some of the dissimilarities between nonlinear and linear differential equations.
Initially let's take a look at a theorem regarding to linear first order differential equations. It is a very significant theorem although we're not going to actually use this for its most significant aspect.