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Re: Exp-Trig Manipulation

• To: mathgroup at smc.vnet.net
• Subject: [mg59388] Re: Exp-Trig Manipulation
• From: "Jens-Peer Kuska" <kuska at informatik.uni-leipzig.de>
• Date: Mon, 8 Aug 2005 03:34:35 -0400 (EDT)
• Organization: Uni Leipzig
• References: <dd4ejd$hls$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

Hi,

e1 = E^((2 - I)*x)*C[1] + E^((2 + I)*x)*C[2] + 
E^((3 - 4*I)*x)*C[3] + E^((3 +
4*I)*x)*C[4] // ComplexExpand

??

Regards

  Jens



"Daniele Lupo" 
<danwolf80_no_spam_please_ at libero.it> schrieb im 
Newsbeitrag news:dd4ejd$hls$1 at smc.vnet.net...
| Hi to everyone.
|
| I'd like to know how I can convert this 
expression
|
| E^((2 - I)*x)*C[1] + E^((2 + I)*x)*C[2] + 
E^((3 - 4*I)*x)*C[3] + E^((3 +
| 4*I)*x)*C[4]
|
| in its equivalent form
|
| E^(2*x)*C[2]*Cos[x] + E^(3*x)*C[4]*Cos[4*x] + 
E^(2*x)*C[1]*Sin[x] +
| E^(3*x)*C[3]*Sin[4*x]
|
|
| I've obtained them while resolving a 
differential equation. I've tried to
| solve this:
|
| car = y''''[x] - 10*y'''[x] + 54*y''[x] - 
130*y'[x] + 125*y[x] == 0;
|
| In two different ways: first, working with 
characteristic polynomial:
|
| -------------------
|
| (* Conversion from differential equation to 
characteristic polynomial *)
|
| pol = car /. {Derivative[n_][y][x] -> ë^n, 
y[x] -> 1};
|
| (* Solutiof of c.p. *)
|
| sol = Solve[pol, ë];
|
| (* Mapping solutions in a linear combination of 
exponentials *)
|
| solution1 = Plus @@ 
MapIndexed[C[#2[[1]]]*Exp[x*#1] & , ë /. %]
|
| -------------------
|
|
| While I've obtained second solution using 
DSolve:
|
|
| -------------------
|
| solution2 = y[x] /. DSolve[car, y[x], x][[1]]
|
| -------------------
|
| So, if I did not wrong something, these two 
solutions must be equivalent,
| but I can't find a way to trasform solution1 to 
solution2: I know that
| there can be a problem in conversion of C[n] 
coefficients during
| transformation, but I don't care it. I'd like 
instead to convert in the
| right way exponentials of first method in right 
product of Cos, Sin, Exp of
| the solution obtained with DSolve.
|
| Thanks for answers
|
| Daniele
|