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