LODEstruct is a data structure to represent an ordinary differential equation. It is created by Slode[DEdetermine].

The entries of an LODEstruct are a set of equations, representing the differential equation, and a set of function names, representing the dependent variables.

The data structure has an attribute table with the following entries:

L - the differential operator in diff notation

rhs - the right hand side of the equation

fun - the name of the dependent variable, for example

var - the name of the independent variable, for example

linear -  if L is a linear differential operator and  otherwise

ord - the order of L

coeffs - an Array of coefficients of L

polycfs -  if all coefficients are polynomial and  otherwise

d_max   - the maximum degree of polynomial coefficients

If the right hand side is a formal power series in the form  where  is a polynomial in ,  is either  or ,  is the expansion point, and  is an expression in , then it is represented as a RHSstruct data structure. The entries of an RHSstruct are the right hand side and the independent variable . In addition, the data structure has an attribute table with following entries:

mvar - the name of the independent variable,

index - the name of the summation index,

point - the expansion point , possibly

M - a nonnegative integer such that series coefficients are equal  for all ; it satisfies

initial - an Array of  initial series coefficients

H - the expression

P_n - either  or