Re: symbolic solution of ODE

*To*: mathgroup at smc.vnet.net*Subject*: [mg71510] Re: symbolic solution of ODE*From*: "ben" <benjamin.friedrich at gmail.com>*Date*: Tue, 21 Nov 2006 07:05:07 -0500 (EST)

Hi I do not know how to teach Mathematica to simplify its result for the cast t^2<k. However you can read off the solution yourself: The two double-sqrt-expressions appearing in the exponent are complex conjugate; just introduce new notation a+bi and a-bi and let Mathematica replace the old by the new notation. Then you "see" the solution immeadiatly C[5] Exp[a z] Cos[b z + C[6]]+C[7] Exp[-a z] Cos[b z + C[8]] Bye Ben the replacement-rule: In[33]:= \!\(\(w[z] /. sol[\([1]\)]\) /. {\@\(t - \@\(\(-k\) + t\^2\)\) \[Rule] a + b\ I, \@\(t + \@\(\(-k\) + t\^2\)\) \[Rule] a - b\ I}\) Out[33]= \!\(\[ExponentialE]\^\(\((a + \[ImaginaryI]\ b)\)\ z\)\ C[ 1] + \[ExponentialE]\^\(\(-\((a + \[ImaginaryI]\ b)\)\)\ z\)\ C[ 2] + \[ExponentialE]\^\(\((a - \[ImaginaryI]\ b)\)\ z\)\ C[ 3] + \[ExponentialE]\^\(\(-\((a - \[ImaginaryI]\ b)\)\)\ z\)\ C[4]\) C[5] Exp[a z] Cos[b z + C[6]]+C[7] Exp[-a z] Cos[b z + C[8]] visbuga at purdue.edu schrieb: > Hello, > > I like to solve the ODE > DSolve[w''''[z] - 2*t*w''[z] + k*w[z] == 0, w[z], z] > by imposing the condition "t^2 < k" on constants in the eqn.In fact, solution > of this homogenous ODE is known, but I want to see the result of mathematica > to use in a complex eqn. Thank you. > > VV