Authors: Claude Michael Cassano
This linear algebra technique provides a useful method of obtaining exact solutions to homogeneous linear ordinary differential equations. The Bessel half integer solutions, being long well known, have been used here to verify with confidence the above linear independence technique for solving ordinary differential equations. The Bessel second order LHODE has been used, here, as an example application of this vector space transformation technique. Clearly, it may be used on other non-general elementary second order LHODE, such as the Legendre, Laguerre, Hermite and other second order LHODE's. Using the two linearly independent solutions of a second order linear homogeneous ordinary differential equations insures that the two functions are linearly independent. However, any two linearly independent functions may be used, and the two resulting differential equations need not be the same, as was the case for the Bessel's above. In fact, clearly, the technique may also be used for higher order LHODE's, since there are N linearly independent solutions of an N-th order LHODE there would be an equal number of transformation equations.
Comments: 10 Pages.
[v1] 2018-04-14 11:41:48
Unique-IP document downloads: 6 times
Vixra.org is a pre-print repository rather than a journal. Articles hosted may not yet have been verified by peer-review and should be treated as preliminary. In particular, anything that appears to include financial or legal advice or proposed medical treatments should be treated with due caution. Vixra.org will not be responsible for any consequences of actions that result from any form of use of any documents on this website.
Add your own feedback and questions here:
You are equally welcome to be positive or negative about any paper but please be polite. If you are being critical you must mention at least one specific error, otherwise your comment will be deleted as unhelpful.