I am going to ask a question this time. I got a hold of the book
Ordinary DE and Stability Theory by Sanchez I picked up for a song. It has some tough problems. I thought it would be a nice book, but the notation is killer.
I have been wanting to strengthen my DE skills.
Here is one if anyone has a good idea.
Let's take the equation , where x=x(t) is an unknown
scalar function and f and df/dx are defined and continuous on the strip
We can also assume ,
and let ,
Show all solutions are described by the family
, where is the inverse
of F, and c is a constant determined by initial conditions.
I tried using the second fundamental theorem of calculus and thought
Just a little hung up.