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MathGroup Archive 2000

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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


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