Please solve the attached problem in the image with work shown, thank you.

I am attaching the image, but if it is not showing, here is an imgur link with the image to the problem as well: https://i.imgur.com/RByR1L3.png

This question is not incomplete, I am presenting it to you exactly how I received it. This is from a nonlinear differential equations class. Please show your work for the problem as well. Please do not mark the question as incomplete as I do not have any further revisions available. Thank you for your help.

1. (20 points) Consider the following nonlinear differential equation, i = e cos(x), :(0) = In (1) Show that the above initial value problem has a unique solution for any To. (2) Sketch the phase portrait, find all fixed points for the above system and classify their stability. (3) Use linear stability analysis to show the stability of point =