       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,

((C + C)*Cos[(Sqrt*x)/2])/E^(x/2)

But the general solution should be:
C*Cos[(Sqrt*x)/2])*E^(-x/2) + C*Sin[(Sqrt*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:= DSolve[y''[x]+y'[x]+y[x]==0,y[x],x]
> >
> >                                    2/3
> >                     C       (-1)    x
> >Out= {{y[x] -> ---------- + E          C}}
> >                       1/3
> >                   (-1)    x
> >                  E
> >
> >-----------------------------------------------------
> >
>
> (y[x] /. DSolve[y''[x] + y'[x] + y[x] == 0, y[x], x][]) // Re //
>     ComplexExpand // Simplify
>
> ((C + C)*Cos[(Sqrt*x)/2])/E^(x/2)
>
>
> Bob Hanlon
>

```

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