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Re: How to avoid complex exponents?


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
> 


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