Re: How to avoid complex exponents?

• To: mathgroup at smc.vnet.net
• Subject: [mg24940] Re: [mg24931] How to avoid complex exponents?
• From: Hugh Walker <hwalker at gvtc.com>
• Date: Thu, 24 Aug 2000 05:08:14 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

```Peter Chan <y6k at hotmail.com> wrote

===============

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

-----------------------------------------------------
==============

If you assume all symbols can be taken as real, then what you want is

y[x] /. DSolve[y''[x] + y'[x] + y[x] == 0, y[x], x] // First // ComplexExpand

==

Hugh Walker
Gnarly Oaks

```

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