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
>