Re: symbolic solution of ODE

• To: mathgroup at smc.vnet.net
• Subject: [mg71514] Re: symbolic solution of ODE
• From: "dimitris" <dimmechan at yahoo.com>
• Date: Tue, 21 Nov 2006 07:05:11 -0500 (EST)
• References: <ejtdfo\$iva\$1@smc.vnet.net>

```Hello.

First the solution of your ODE.

sol = DSolve[Derivative[4][w][z] - 2*t*Derivative[2][w][z] + k*w[z] ==
0, w[z], z, GeneratedParameters -> (Subscript[c, #1] & )]

Let's check it.

derfun = Flatten[(D[sol, {z, #1}] & ) /@ Range[0, 4]];

FullSimplify[Derivative[4][w][z] - 2*t*Derivative[2][w][z] + k*w[z] ==
0 //. %]
True

>...imposing the condition "t^2 < k"...

Did you mean something like the following?

w[z] /. FullSimplify[sol /. -k + t^2 -> -m^2, m > 0][[1]]

Dimitris

visbuga at purdue.edu wrote:
> 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

```

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