Re: DSolve for a real function

*To*: mathgroup at smc.vnet.net*Subject*: [mg127939] Re: DSolve for a real function*From*: Andreas Talmon l'Armée at smc.vnet.net*Date*: Tue, 4 Sep 2012 05:45:06 -0400 (EDT)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com*Delivered-to*: l-mathgroup@wolfram.com*Delivered-to*: mathgroup-newout@smc.vnet.net*Delivered-to*: mathgroup-newsend@smc.vnet.net*References*: <k1k8np$90f$1@smc.vnet.net> <20120901062746.B3D7F687B@smc.vnet.net>

Hi, My initial conditions are the following and I am pretty sure that my solution consists only of a real part. The Solution has four eigenvalues and they are complex conjugated. With all variables and all parameters real numbers I must be able to retrieve a real solution. But being a mathematica newbie, I do not understand how to do it with mathematca. y''[-c] == ic0, y''[c] == ic0, y'''[-c] == ic1, y'''[c] == -ic1 My Notebook is also ready for download at dropbox.com: http://dl.dropbox.com/u/4920002/DGL_4th_Order.nb Clear[sol] $Assumptions = {a \[Element] Reals, ic0 \[Element] Reals, ic1 \[Element] Reals, c \[Element] Reals}; sol[a_, x_] = y[x] /. DSolve[{y''''[x] + a y[x] == 0, y''[-c] == ic0, y''[c] == ic0, y'''[-c] == ic1, y'''[c] == -ic1}, y[x], x][[1]] // FullSimplify Reduce[Element[sol[a, x], Reals], a, Reals] Thanks for your help, Andreas On 09/01/2012 08:27 AM, Bob Hanlon wrote: > 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 >>

**References**:**Re: DSolve for a real function***From:*Bob Hanlon <hanlonr357@gmail.com>