ABSTRACT
Any ordinary differential equation in which the independent variable does not appear explicitly is an autonomous equation. Linear constant coefficient ordinary differential equations have solutions that are either exponentials or exponentials multiplied by polynomials. The method of undetermined coefficients can be used to solve this type of equation; the roots of a polynomial will have to be determined. Composing two contact transformations or taking the inverse of a contact transformation results in another contact transformation. The method of generating functions is frequently used when only integral values of the variables are of interest. Any “well-behaved” function can be expanded in a complete set of eigenfunctions.
