📖 Smoothness of Polynomials. With Respect to Boundary Conditions As Solutions of Ordinary Differential Equations.

In this book, we are interested in the smooth dependence of polynomial solutions of linear ordinary differential equations to their specific boundary conditions. We investigate the case for the solutions of y?? = 0 and y??? = 0 to observe the smooth dependence. Once we notice a pattern, we generalize the results into a theorem. Finally, we discuss possible applications and extensions of the results.