Math 224-01: Differential Equations: Reading Homework 3.3

1. Undriven Constant Coefficient Linear ODEs, I : what do each of the terms describing ``ODEs'' in this title say about the differential equations?
   
   1. Finding Solution Formulas : how might we find a solution to y'' + ay' + by = 0?
      
      1. Point : what is the solution guess for this type of problem?
         
      2. Point : what are the characteristic polynomial and roots for a constant-coefficient linear ODE?
         
      3. Point : how are the solutions found using our guess combined to obtain a general solution to the ODE?
         
      4. Point : what is the solution to a linear constant-coefficient ODE whose characteristic equation has real roots?
         
   2. the Differentiation Operator : what is the differentiation operator D? what are D[3y] and (D-4)[e^t]?
      
   3. Properties of D : how might we remember operator identities?
      
      1. Point : what is a polynomial operator? the characteristic polynomial of one?
         
      2. Point : what properties does a polynomial operator have? what's a linear operator?
         
      3. Point : how can we use factoring an operator to solve a driven ODE?