Services & Resources / Wolfram Forums
-----
 /
MathGroup Archive
2000
*January
*February
*March
*April
*May
*June
*July
*August
*September
*October
*November
*December
*Archive Index
*Ask about this page
*Print this page
*Give us feedback
*Sign up for the Wolfram Insider

MathGroup Archive 2000

[Date Index] [Thread Index] [Author Index]

Search the Archive

Re: How to avoid complex exponents?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg24947] Re: [mg24931] How to avoid complex exponents?
  • From: "Peter Chan" <y6k at hotmail.com>
  • Date: Thu, 24 Aug 2000 05:08:18 -0400 (EDT)
  • References: <50.9ef5b3d.26d46f90@aol.com>
  • Sender: owner-wri-mathgroup at wolfram.com

Hello Bob,

Thank you for your help.

Your solution gives:
((C[1] + C[2])*Cos[(Sqrt[3]*x)/2])/E^(x/2)

But the general solution should be:
C[3]*Cos[(Sqrt[3]*x)/2])*E^(-x/2) + C[4]*Sin[(Sqrt[3]*x)/2])*E^(-x/2)


Peter

> 
> In a message dated 8/22/2000 4:42:25 PM, y6k at hotmail.com writes:
> 
> >What is the simplest way to avoid the complex exponents, i.e.
> >exp((-1)^(1/3))
> >and exp((-1)^(2/3)), given by Mathematica 4.0 in the solution of the
> >following
> >differential equation?
> >
> >Thanks.
> >
> >-----------------------------------------------------
> >Mathematica 4.0 :
> >
> >In[1]:= DSolve[y''[x]+y'[x]+y[x]==0,y[x],x]
> >
> >                                    2/3
> >                     C[1]       (-1)    x
> >Out[1]= {{y[x] -> ---------- + E          C[2]}}
> >                       1/3
> >                   (-1)    x
> >                  E
> >
> >-----------------------------------------------------
> >
> 
> (y[x] /. DSolve[y''[x] + y'[x] + y[x] == 0, y[x], x][[1]]) // Re //
>     ComplexExpand // Simplify
> 
> ((C[1] + C[2])*Cos[(Sqrt[3]*x)/2])/E^(x/2)
> 
> 
> Bob Hanlon
> 


  • Prev by Date: Re: functional routine for {a, b, c, ...} -> {a - b, b - c, c - ...}
  • Next by Date: RE:Email
  • Previous by thread: Re: How to avoid complex exponents?
  • Next by thread: Re: How to avoid complex exponents?