The paper deals with the higher-order ordinary differential equations and the analogous higher-order difference equations and compares the corresponding fundamental concepts. Important dissimilarities appear for the moving frame method.

Let k be a field of characteristic zero. We describe the kernel of any quadratic homogeneous derivation d:k[x,y,z] → k[x,y,z] of the form $d=x(Cy+z)\frac{\partial }{\partial x}+y(Az+x)\frac{\partial }{\partial y}+z(Bx+y)\frac{\partial }{\partial z}$, called the Lotka-Volterra derivation, where A,B,C ∈ k.