Solved

# help with differential euqation

Posted on 2014-04-24
169 Views
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
Question by:c_hockland

LVL 27

Expert Comment

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

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

A Guide to the PMT, FV, IPMT and PPMT Functions In MS Excel we have the PMT, FV, IPMT and PPMT functions, which do a fantastic job for interest rate calculations.  But what if you don't have Excel ? This article is for programmers looking to re…
We are taking giant steps in technological advances in the field of wireless telephony. At just 10 years since the advent of smartphones, it is crucial to examine the benefits and disadvantages that have been report to us.
Here's a very brief overview of the methods PRTG Network Monitor (https://www.paessler.com/prtg) offers for monitoring bandwidth, to help you decide which methods you´d like to investigate in more detail.  The methods are covered in more detail in o…
This video shows how to remove a single email address from the Outlook 2010 Auto Suggestion memory. NOTE: For Outlook 2016 and 2013 perform the exact same steps. Open a new email: Click the New email button in Outlook. Start typing the address: …