Introduction

This gives detailed description of all supported differential equations in my step-by-step ode solver. Whenever possible, each ode type algorithm is described using flow chart.

Each ode type is given an internal code name. This internal code is used internally by the solver to determine which solver to call to solve the specific ode.

The following is the top level chart of supported solvers.

Figure 1: Top level flow chart for ode solver

This diagram illustrate some of the plots generated for direction field and phase plots.

Figure 2: Direction and slope fields generated

For a differential equation, there are three types of solutions

1. General solution. This is the solution \(y(x)\) which contains arbitrary number of constants up to the order of the ode.
2. Particular solution. This is the general solution after determining specific values for the constant of integrations from the given initial or boundary conditions. This solution will then contain no arbitrary constants.
3. singular solutions. These are solutions to the ode which satisfy the ode itself and contain no arbitrary constants but can not be found from the general solution using any specific values for the constants of integration. These solutions are found using different methods than those used to finding the general solution. Singular solution are hence not found from the general solution like the case is with particular solution.