# Recent content by tobythetrain

1. ### Poincarè stabillity!

Thanks for replying on this subject, Alan2, I do apreciate it! That's actually the first result I got, but i realized that it would not give the max value of any trajectory starting fra the small circle. My logic told me that the trajectory I was looking for did not start in (-1,δ), but in a...
2. ### Poincarè stabillity!

Hey Guys! I'm having MAJOR difficulty with a problem regarding stability of a DE. The problem goes as following: Find the equation of the phase paths of x˙=1+x^2, y˙=−2xy. It is obvious from the phase diagram that y=0 is Poincaré stable. Show that for the path y=0, all paths which start in...
3. ### Sum of infinite series

2. I tried to write the integralsign, but couldnt find it so I did it the easy way... I totally see it now, and my problem is solved. Thanks alot for helping me! This is a wonderful forum! Toby
4. ### Sum of infinite series

Homework Statement Given the Infinite Series 1/(1+n^2) where n goes from 1 to infinity, show that the sum is less than pi/2. Homework Equations 1/(1+n^2)dx=arctanx Series goes 1/2, 1/5, 1/10, 1/17, 1/26 and so on The Attempt at a Solution I have tried to find a telescoping...