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
 Horng-Jaan Li and Cheh-Chih Yeh, On the nonoscillatory behavior of solutions of a second order linear differential equation
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 .
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