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Re: Simple DSolve equation

  • To: mathgroup at smc.vnet.net
  • Subject: [mg122631] Re: Simple DSolve equation
  • From: Rui Rojo <rui.rojo at gmail.com>
  • Date: Fri, 4 Nov 2011 05:59:09 -0500 (EST)
  • Delivered-to: l-mathgroup@mail-archive0.wolfram.com
  • References: <201111030846.DAA15245@smc.vnet.net>

What I want to somehow get is the most general result with restrictions
over k. That is:

{y''[x] == k y[x], y[0] == 0, y[10] == 0} /. {
   y -> (Sin[2 Pi p/20 #] &),
   k -> -(1/100) p^2 \[Pi]^2 }
Out: {True, True, Sin[p \[Pi]] == 0}
Simplify[%, p \[Element] Integers]
{True, True, True}
...or any linear combination of those solutions. Typical 10m rope tied on
the extremes

2011/11/3 Bob Hanlon <hanlonr357 at gmail.com>

> soln = DSolve[{y''[x] == k y[x], y[0] == y0, y[10] == y10}, y[x], x][[1,
> 1]]
>
> y[x] -> (E^(20*Sqrt[k])*y0 - E^(2*Sqrt[k]*x)*y0 - E^(10*Sqrt[k])*y10 +
>        E^(10*Sqrt[k] + 2*Sqrt[k]*x)*
>     y10)/(E^(Sqrt[k]*x)*(-1 + E^(20*Sqrt[k])))
>
> soln /. y0 -> 0 // Simplify
>
> y[x] -> ((-1 + E^(2*Sqrt[k]*x))*
>    y10)/(E^(Sqrt[k]*(-10 + x))*(-1 + E^(20*Sqrt[k])))
>
> soln /. y10 -> 0 // Simplify
>
> y[x] -> ((E^(20*Sqrt[k]) - E^(2*Sqrt[k]*x))*
>    y0)/(E^(Sqrt[k]*x)*(-1 + E^(20*Sqrt[k])))
>
> soln /. {y0 -> 0, y10 -> 0}
>
> y[x] -> 0
>
> What solution are you expecting?
>
>
> Bob Hanlon
>
>
> On Thu, Nov 3, 2011 at 4:46 AM, Rui <rui.rojo at gmail.com> wrote:
> > Why does something like this not give the correct answer with
> restrictions over k?
> > How would you go about getting the right general solutions in these kind
> of basic differential equations?
> >
> > Thanks
> >
> > DSolve[{y''[x] == k y[x], y[0] == 0, y[10] == 0}, y[x], x]
> > Out={{y[x] -> 0}}
> >
>



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