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For the sake of simplicity, in the sequel a (Laurent) polynomial of negative degree is understood to be the zero polynomial and, similarly, a banded matrix with negative bandwidth reduces to the zero matrix.
A polynomial P(v) with all terms having degree n is homogeneous as P(Av) = AnP(v) for all vectors v and scalars A. A differential equation of the form dy/dx = M(x,y) / N(x,y) is homogeneous if M and N are homogeneous of the same degree. Proof: Let M and N be both homogeneous polynomials of degree K.