The main role is played by the second order

linear differential equation which these polynomials satisfy since this yields the electrostatic interpretation.

Let us consider the first order

linear differential equation for [??],

[17] Horng-Jaan Li and Cheh-Chih Yeh, On the nonoscillatory behavior of solutions of a second order

linear differential equation, Math.

Third-Order

Linear Differential Equation with Oscillating and Nonoscillating Solutions

Sun, "Hyers-Ulam stability of

linear differential equations of first order," Applied Mathematics Letters, vol.

First of all, we consider the complex dynamical properties of solutions to second order

linear differential equations with polynomial coefficients and obtain the following two remarks.

Xu, "Hyers-Ulam stability of a class of fractional

linear differential equations," Kodai Mathematical Journal, vol.

To overcome this problem, an analytical approach is used, which converts the original nonlinear differential equation to a

linear differential equation, that can be solved in closed form at each time step [14].

According to Olver [8], although most of Lie's work was concerned with first order

linear differential equation systems, he also studied the problem of determining the symmetries of second order partial differential equations in two independent and one dependent variables; in particular, Lie found the heat equation symmetries, a case that has been taken for several authors as a key example for the description of the method.

As noted above, in Section 5.1 we determine a particular solution of a non-homogeneous

linear differential equation with piecewise constant coefficients and piecewise continuous right side.

This is easy to verify by solving or simulating the

linear differential equation (3c) relative to [M.sub.B](t).

which is theso-called areolar

linear differential equation [9, pp.