The linear differential equation whose solutions are the products of solutions of two given differential equations

AbstractA linear homogeneous ODE is constructed, among whose solutions are all products of solutions of two given linear homogeneous ODE's Lm[u]=0, Mn[v]=0, in some classes. Its order is the minimum and its coefficients can be obtained by a finite number of rational operations and differentiations on the coefficients of Lm, Mn. The problem is considered (locally) both in the real and in the complex domain, around an isolated singularity. Examples are also given