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MathGroup Archive 2000

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Re: How to avoid complex exponents?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg24978] Re: [mg24931] How to avoid complex exponents?
  • From: Murray Eisenberg <murray at math.umass.edu>
  • Date: Mon, 28 Aug 2000 08:27:37 -0400 (EDT)
  • Organization: Mathematics & Statistics, Univ. of Mass./Amherst
  • References: <50.9ef5b3d.26d46f90@aol.com> <94mp5.21835$Ok.18227@ralph.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

Use Im similarly to the way Bob Hanlon used Re on the complex
exponential, then form the linear combination?

Peter Chan wrote:
> 
> 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
> >

-- 
Murray Eisenberg                     murray at math.umass.edu
Mathematics & Statistics Dept.       phone 413 549-1020 (H)
Univ. of Massachusetts                     413 545-2859 (W)
Amherst, MA 01003-4515


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