Re: How to avoid complex exponents?
- To: mathgroup at smc.vnet.net
- Subject: [mg24941] Re: [mg24931] How to avoid complex exponents?
- From: BobHanlon at aol.com
- Date: Thu, 24 Aug 2000 05:08:15 -0400 (EDT)
- Sender: owner-wri-mathgroup at wolfram.com
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