1.1 Types of solutions supported

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.

The solver currently finds the general and Particular solution (if initial conditions are given). It also finds singular solutions but for very limited first order ode’s. More support for finding singular solutions using the p-discriminant and c-discriminant methods will be added.