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    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...
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    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...