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.
This diagram illustrate some of the plots generated for direction field and phase
plots.
For a differential equation, there are three types of solutions
General solution. This is the solution \(y(x)\) which contains arbitrary number of
constants up to the order of the ode.
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.
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.