Solved

help with differential euqation

Posted on 2014-04-24
4
173 Views
Last Modified: 2014-05-03
I reading the solution of a dif eq
Y'' -m^2 *n^2 * y =

Y = c1e1 ^ ( -mny) + c2e2 ^ ( + mny )
how did he get this result ?

and X'' + n^2X
then X = c3 sin nx + c4 cosnx
0
Comment
Question by:c_hockland
4 Comments
 
LVL 27

Expert Comment

by:d-glitch
ID: 40022534
Could you post a scan or photo of the actual equations?

I still might not be able to help, but the text form of complex math is an additional and unpleasant hurdle.
0
 
LVL 27

Accepted Solution

by:
BigRat earned 500 total points
ID: 40022813
Taking the second equation first, y'' + n²y = 0, and substitute y = A*exp(bt) you get :-

      A*b*b*exp(bt) + n²*A*exp(bt) = 0

and this can only be so if b²=-n² and this only if b = i*n where i is the square root of -1.
(Because e to the power of anyting is NEVER zero, and A=0 is a tribial solution)

And n can be positive of negative, since it square is aloways positive, so the exponentials are exp(int) and exp(-int), and it you remember your trig, this is sin(nt) and cos(nt) and hence the result.

So back into the first equation where n² is m²*n² and presto the result.
0

Featured Post

ScreenConnect 6.0 Free Trial

Check out the updates in one game-changing release, ScreenConnect 6.0, based on partner feedback. New features include a redesigned UI that improves session organization and overall user experience. See the enhancements for yourself!

Question has a verified solution.

If you are experiencing a similar issue, please ask a related question

Suggested Solutions

Title # Comments Views Activity
how to find inverse of a nxn matrix when n is large ie n=8,10... 9 43
How to onstruct a table 4 49
Standard Deviation 2 36
Interest rate formula 7 66
How to Win a Jar of Candy Corn: A Scientific Approach! I love mathematics. If you love mathematics also, you may enjoy this tip on how to use math to win your own jar of candy corn and to impress your friends. As I said, I love math, but I gu…
This article provides a brief introduction to tissue engineering, the process by which organs can be grown artificially. It covers the problems with organ transplants, the tissue engineering process, and the current successes and problems of the tec…
This is a video describing the growing solar energy use in Utah. This is a topic that greatly interests me and so I decided to produce a video about it.
Although Jacob Bernoulli (1654-1705) has been credited as the creator of "Binomial Distribution Table", Gottfried Leibniz (1646-1716) did his dissertation on the subject in 1666; Leibniz you may recall is the co-inventor of "Calculus" and beat Isaac…

778 members asked questions and received personalized solutions in the past 7 days.

Join the community of 500,000 technology professionals and ask your questions.

Join & Ask a Question