Math 224-01: Differential Equations: Reading Homework 2.2

1. Extension and Long-Term Behavior : how might we try and determine the length of the interval a solution is defined on? what else might we be interested in seeing about the solution curves?
   
   1. Existence : what is an extension of a solution to an ODE?
      
      1. maximal extension : how far are we guaranteed to be able to extend a solution?
         
      2. death of a solution : when may a solution ``die''? what is the characteristic of a direction field there?
         
      3. escape time : what is a finite escape time?
         
   2. Sign analysis, State lines : can a non-autonomous ODE have an equilibrium solution? what is the translation property of autonomous ODEs?
      
      1. sign analysis : what is sign analysis?
         
      2. state lines : what is a state line?
         
      3. steady states : what is a steady state solution? how is it different from an equilibrium solution?