Chapter Summaries
1.1 Hierarchy of Differential Equations:
Note: in each category, difficulty of solution decreases...
  1. Partial Differential Equations (>1 independent variable)
    1. System (>1 equation)
      1. Nonlinear
        1. Higher Order
        2. First Order
      2. Linear
        1. Higher Order
        2. First Order
    2. Single Equation (1 equation)
      1. Nonlinear
        1. Higher Order
        2. First Order
      2. Linear
        1. Higher Order
        2. First Order
  2. Ordinary Differential Equations (1 independent variable)
    1. System (>1 equation)
      1. Nonlinear
        1. Higher Order
        2. First Order
      2. Linear
        1. Higher Order
        2. First Order
    2. Single Equation (1 equation)
      1. Nonlinear
        1. Higher Order
        2. First Order
      2. Linear
        1. Higher Order
        2. First Order
1.2 There are two types of solutions: explicit and implicit