Re: Boundary Value Problem

• To: mathgroup at smc.vnet.net
• Subject: [mg6903] Re: Boundary Value Problem
• From: Stephen P Luttrell <luttrell at signal.dra.hmg.gb>
• Date: Fri, 25 Apr 1997 14:00:35 -0400 (EDT)
• Organization: Defence Research Agency
• Sender: owner-wri-mathgroup at wolfram.com

```> y'''''[x]+y[x]==0
>
> Conditions
> y[0]==0
> y'[0]==7
>
> y[1]==1
> y'[1]==10
> y''[1]=5
>

Try the following input (I use Mathematica 3.0)

DSolve[{D[y[x],{x,5}]+y[x]==0,y[0]==0,D[y[x],{x,1}][0]==7,y[1]==1,
D[y[x],{x,1}][1]==10,D[y[x],{x,2}][1]==5},y[x],x]

It gives the following warning (I don't know why)

DSolve::"nvld":
"The description of the equations appears to be ambiguous or
invalid."

It then goes on to give the solution (which I haven't simplified)

{{y[x] -> E^(-x - (-1)^(2/5)*x - (-1)^(4/5)*x)*
(E^(x + (-1)^(1/5)*x + (-1)^(2/5)*x + (-1)^(4/5)*x)*
C[2] + E^
(x + (-1)^(2/5)*x + (-1)^(3/5)*x + (-1)^(4/5)*x)*
C[4] + E^(x + (-1)^(2/5)*x)*C[5] +
1/(-E + E^(-1)^(2/5))*
E^((-1)^(2/5) + x + (-1)^(4/5)*x)*
(-E + (-1 + E^(1 + (-1)^(1/5)))*C[2] +
(-1 + E^(1 + (-1)^(3/5)))*C[4] - C[5] +
E^(1 - (-1)^(4/5))*C[5]) +
1/(-E + E^(-1)^(2/5))*
E^(1 + (-1)^(2/5)*x + (-1)^(4/5)*x)*
(E^(-1)^(2/5) + C[2] -
E^((-1)^(1/5) + (-1)^(2/5))*C[2] + C[4] -
E^((-1)^(2/5) + (-1)^(3/5))*C[4] + C[5] -
E^((-1)^(2/5) - (-1)^(4/5))*C[5]))}}

It appears to satisfy your differential equation and its boundary
conditions.

===================================================================

Dr Stephen P Luttrell                  luttrell at signal.dra.hmg.gb