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