       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
> y'==7
>
> y==1
> y'==10
> y''=5
>

Try the following input (I use Mathematica 3.0)

DSolve[{D[y[x],{x,5}]+y[x]==0,y==0,D[y[x],{x,1}]==7,y==1,
D[y[x],{x,1}]==10,D[y[x],{x,2}]==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 + E^
(x + (-1)^(2/5)*x + (-1)^(3/5)*x + (-1)^(4/5)*x)*
C + E^(x + (-1)^(2/5)*x)*C +
1/(-E + E^(-1)^(2/5))*
E^((-1)^(2/5) + x + (-1)^(4/5)*x)*
(-E + (-1 + E^(1 + (-1)^(1/5)))*C +
(-1 + E^(1 + (-1)^(3/5)))*C - C +
E^(1 - (-1)^(4/5))*C) +
1/(-E + E^(-1)^(2/5))*
E^(1 + (-1)^(2/5)*x + (-1)^(4/5)*x)*
(E^(-1)^(2/5) + C -
E^((-1)^(1/5) + (-1)^(2/5))*C + C -
E^((-1)^(2/5) + (-1)^(3/5))*C + C -
E^((-1)^(2/5) - (-1)^(4/5))*C))}}

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

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

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