Discipline: Mathematics and Statistics
Subcategory: Mathematics and Statistics
Session: 2
Asia Q. Bryant - Texas Southern University
Co-Author(s): Dr. W.E. Taylor, Texas Southern University, Houston, TX
In this research, the equations studied are y000+ay0+by= 0(E)andy000+ax2y0+bx3y= 0:(Eu)Equation (E) has constant coecients while equation (Eu) is an Euler dif-ferential equation and has variable coecients. Solutions of these equationswill be studied with respect to their oscillatory behavior according to whether the constantsaorbhave the same sign or opposite signs. Both similar and contrasting behavior will be examined.
Funder Acknowledgement(s): Thanks to Professor Emeritus L. L. Clarkson for his generous donation to this research experience. . LSAMP Program for their donation, support, and encouragement.
Faculty Advisor: Dr. W.E. Taylor and Dr. Roderick Holmes, Willie.Taylor@tsu.edu
Role: Throughout this work we consider the solutions of (E) and (Eu). The domain of these solutions will be I= (0, infinity). Our results apply to non-trivial solutions of these equations. Solutions of (E) and (Eu) are called oscillatory if they have an infinite number of zeros and non-oscillatory otherwise. Thus,a non-oscillatory solution is eventually positive or eventually negative. To obtain solutions to (E) and (Eu) respectively we let y=e^mx and y=x^m.From these substitutions we obtain two polynomial equations, called characteristic equations for (E) and (Eu). It was my responsibility to manually do the math to find the solutions that would make each equation true and to find the similarities and differences between the two. I did this through function dynamics.