The question . Differential equations , linear and non linear , of any type or degree . f(t) = some function , with or without constants . D(f(t)) = some differential equation involving f(t) , f'(t) and other . The condition that we want to satisfy is : D(f(t)) = 0 To do so , at the most basic level , we need to generate a large set of functions where there's a function that satisfies : D(f(t)) = 0 This is what I'm attempting to do with xfractint . Symbolically we tend to do things like finding an integrating factor , finding symmetries via lie algebras , performing iterated integration like He's Variational Iteration Method , fractional integration and a fair few others . To the best of my knowledge none of these are applicable to the full gamut of fractals or even the subset of all non linear differential equations ; which tend to be the most interesting . Just wondering if anyone has some suggestions , I continue to have this feeling that previous contributors to fractint formulas had some notion as to what might be involved with this .