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MathGroup Archive 2000

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Re: real valued solutions?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg23492] Re: [mg23449] real valued solutions?
  • From: BobHanlon at aol.com
  • Date: Fri, 12 May 2000 22:54:30 -0400 (EDT)
  • Sender: owner-wri-mathgroup at wolfram.com

In a message dated 5/10/2000 2:55:33 AM, robert.schuerhuber at gmx.at writes:

>i guess my problem is rather simple to solve, but i counld't figure it
>out :-(
>
>i'd like to solve ordinary differential equations with constant
>coefficients with mathematica, where everything is real-valued. so the
>solution is real-valued, too. how can i avoid the complex exponentials
>in the solution?
>
>e.g.
>
>DSolve[{y''[x]-y'[x]+y[x]==0,y[0]==1,y'[0]==0},y[x],x]
>
>gives
>
>{{y[x]->Exp[-(-1)^2/3 x ( ... }}
>
>as the result instead of the real-valued solution y[x]=Exp[x/2]
>(Cos[Sqrt[3]/2 x]-1/Sqrt[3] Sin[Sqrt[3]/2 x).
>

y[x] /. Flatten[
        DSolve[{y''[x] - y'[x] + y[x] == 0, y[0] == 1, y'[0] == 0}, y[x], 
          x]] // ComplexExpand // Simplify

-(1/3)*E^(x/2)*(Sqrt[3]*Sin[(Sqrt[3]*x)/2] - 
   3*Cos[(Sqrt[3]*x)/2])


Bob

BobHanlon at aol.com


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