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Re: DSolve for a real function

• To: mathgroup at smc.vnet.net
• Subject: [mg127919] Re: DSolve for a real function
• From: Bob Hanlon <hanlonr357 at gmail.com>
• Date: Sat, 1 Sep 2012 02:27:46 -0400 (EDT)
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• References: <k1k8np$90f$1@smc.vnet.net>

What are your initial conditions?

Clear[sol]

sol[a_, x_] = y[x] /. DSolve[
     {y''''[x] + a y[x] == 0,
      y[0] == ic0, y'[0] == ic1,
      y''[0] == ic2, y'''[0] == ic3},
     y[x], x][[1]] // FullSimplify

(1/(2*a^(3/4)))*
   (Cosh[(a^(1/4)*x)/Sqrt[2]]*
        (2*a^(3/4)*ic0*Cos[(a^(1/4)*x)/
                 Sqrt[2]] + Sqrt[2]*
             (Sqrt[a]*ic1 + ic3)*
             Sin[(a^(1/4)*x)/Sqrt[2]]) +
      (Sqrt[2]*(Sqrt[a]*ic1 - ic3)*
             Cos[(a^(1/4)*x)/Sqrt[2]] +
           2*a^(1/4)*ic2*Sin[(a^(1/4)*x)/
                 Sqrt[2]])*
        Sinh[(a^(1/4)*x)/Sqrt[2]])

Reduce[Element[sol[a, x], Reals], a, Reals]

a > 0


Bob Hanlon


On Fri, Aug 31, 2012 at 3:59 AM,  <"Andreas Talmon l'Arm=E9e"@smc.vnet.net> wrote:
> Hi All
>
> Is there a way to tell mathematica to solve only for real solutions. My
> differential equation is of the kind
>
> y''''[x]+a y[x]==0
>
> a= constant coefficient
>
> I know that I get 4 komplex eigenvalues which are complex conjungated.
> But y[x] is a real function.
> Solving this equation with DSolve always gets a complex function y[x].
>
> Any Ideas.
>
> Thanks, Andreas
>

• Follow-Ups:
  • Re: DSolve for a real function
    • From: Andreas Talmon l'Armée@smc.vnet.net