Math 224-01: Differential Equations: Reading Homework 3.2

1. Second-Order ODEs and Their Properties : what can we say about existence, uniqueness, etc. for second-order IVPs? how many state variables do we have for second-order ODEs?
   
   1. Second-Order ODEs : what's the normal form for a second-order IVP? what is the fundamental theorem for second-order ODEs? how is it different from that for first-order ODEs?
      
      1. Point : what is a solution curve for a second-order IVP?
         
      2. Point : what are component curves?
         
      3. Point : what are orbits and the state plane?
         
      4. Point : what is a time-state curve of an ODE?
         
   2. Properties of Solutions : which of time-state curves, solution curves, or orbits of a second-order ODE may intersect? how are the properties of autonomous second-order ODEs different?