rheology, differential equation, buckling, Rodrigues formula. 

Cauchy problem for differential equations can be generalized to arbitrary order derivatives of functions included in the initial conditions. The point of instability is defined as a condition of degeneracy of such statement. The existence of sequence of singular points that are zeros of some system functions is proved. The recurrence relation and the equation of Rodrigues are given for them. The theorem of separation of zeros is proved. Hermite polynomials are special cases of the obtained functions. Based on the proposed theory the phenomenon of buckling of ideal rheological system is analysed.