This post is just a note on the notation that is used across internet sources and books while referring to the LDE.
If one takes , then it follows that . The differential equation can be rewritten as follows:
Now the first two terms must seem familiar to you from the chain rule. ( ). Ergo,
Now, putting back the value of p :
And you will see this form of the LDE also in many places and I thought it was worth mentioning how one ended up in that form.