5.1.2 Examples how to determine which case the ode belongs into

5.1.2.1 Example 1
5.1.2.2 Example 2
5.1.2.3 Example 3
5.1.2.4 Example 4
5.1.2.5 Example 5
5.1.2.6 Example 6
5.1.2.7 Example 7
5.1.2.8 Example 8