1 Introduction
  1.1 Examples how to determine which case the ode belongs into
   1.1.1 Example 1
   1.1.2 Example 2
   1.1.3 Example 3
   1.1.4 Example 4
   1.1.5 Example 5
   1.1.6 Example 6
   1.1.7 Example 7
   1.1.8 Example 8
 2 Examples of ODE’s for each case
 3 Algorithm implementation based on original Kovacic 1985 paper
  3.1 Case one algorithm
   3.1.1 Step 1
   3.1.2 Step 2
   3.1.3 Step 3
   3.1.4 Case one algorithm diagram
  3.2 worked examples for case one
   3.2.1 Example 1
   3.2.2 Example 2
   3.2.3 Example 3
   3.2.4 Example 4
   3.2.5 Example 5
   3.2.6 Example 6
   3.2.7 Example 7
   3.2.8 Example 8
   3.2.9 Example 9
   3.2.10 Example 10
   3.2.11 Example 11
   3.2.12 Example 12
   3.2.13 Example 13
   3.2.14 Example 14
   3.2.15 Example 15
  3.3 Case two Kovacic algorithm
  3.4 Case 3 Kovacic algorithm
 4 Algorithm implementation based on modified Saunders and Smith algorithm
   4.0.1 Step 0
   4.0.2 Step 1
   4.0.3 Step 2
   4.0.4 step 3
  4.1 Worked examples
   4.1.1 Example 1 case one
   4.1.2 Example 2 case one
   4.1.3 Example 3 case one
   4.1.4 Example 4 case one
   4.1.5 Example 5 case one
   4.1.6 Example 6 case one
   4.1.7 Example 7 case two
   4.1.8 Example 8 case two
   4.1.9 Example 9 case two
   4.1.10 Example 10 case two
   4.1.11 Example 11 case one
   4.1.12 Example 12 case one
   4.1.13 Example 13 case one
 5 Notation mapping between Saunders/Smith algorithm and original Kovacis algorithm
 6 References