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Re: Simple DSolve equation
*To*: mathgroup at smc.vnet.net
*Subject*: [mg122643] Re: Simple DSolve equation
*From*: Rui Rojo <rui.rojo at gmail.com>
*Date*: Fri, 4 Nov 2011 06:01:20 -0500 (EST)
*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com
*References*: <201111030846.DAA15245@smc.vnet.net>
Yeah, I didn't know how to ask for restrictions on k...
Those solutions for k aren't all. Something like
k-> -((121 \[Pi]^2)/100) or any k->-((pp^2\[Pi]^2)/100) with pp integer
works.
I still hope for a better solution, I thnk it's a rather basic problem.
If I use reduce instead of Solve where you used solve, then I get a
probably better solution that I'll spend my life reading.
Actually, I am only interested in real solutions, so even if I can't find
the Log[...] solutions DrMajorBob gave me, I'll be fine. If I used reduce
or solve over the Reals domain, I only get the trivial solution m=0, k>0...
Furthermore, if instead of using y[0] and y'[0] as parameters in DSolve I
had used y[0] and y[10] as Bob Hanlon did I would have got a "general"
solution that simplifies to 0 when those parameters are forced to be 0, no
matter k. I mean, you had to get creative and try around because I can't
find a reason to anticipate that writing y'[0]=m can make it work but
y[10]=y10 not.
Normally I wouldn't have problems just messing around until I found the
solution, but, isn't this problem too basic for that? DSolve can solve
Furthermore, even mesing around, I was hoping in the near future to be able
to find (at least some) values of k with not exactly that differential
equation but another one that has to be solved numerically. Now I'm aiming
lower to at least understand how this all works and why it doesn't...
Thask a lot everyone
On Thu, Nov 3, 2011 at 2:54 PM, DrMajorBob <btreat1 at austin.rr.com> wrote:
> a) The solution given is correct, and
>
> b) You gave no restrictions on k. Nor did you ask for any, in Mathematica.
>
> Here's a possible way to go about it:
>
> Clear[y, k, m]
> y =
> y /. First@DSolve[{y''[x] == k y[x], y[0] == 0, y'[0] == m}, y, x]
>
> Function[{x}, (E^(-Sqrt[k] x) (-1 + E^(2 Sqrt[k] x)) m)/(2 Sqrt[k])]
>
> s1 = Quiet@Solve[y[10] == 0, {m, k}]
> y[10] /. s1
> Length@%
>
> {{k -> -\[Pi]^2}, {k -> -((81 \[Pi]^2)/100)}, {k -> -((16 \[Pi]^2)/
> 25)}, {k -> -((49 \[Pi]^2)/100)}, {k -> -((9 \[Pi]^2)/
> 25)}, {k -> -(\[Pi]^2/4)}, {k -> -((4 \[Pi]^2)/25)}, {k -> -((
> 9 \[Pi]^2)/100)}, {k -> -(\[Pi]^2/25)}, {k -> -(\[Pi]^2/
> 100)}, {k -> Log[-(-1)^(1/10)]^2}, {k ->
> Log[-(-1)^(1/5)]^2}, {k -> Log[-(-1)^(3/10)]^2}, {k ->
> Log[-(-1)^(2/5)]^2}, {k -> Log[-(-1)^(3/5)]^2}, {k ->
> Log[-(-1)^(7/10)]^2}, {k -> Log[-(-1)^(4/5)]^2}, {k ->
> Log[-(-1)^(9/10)]^2}, {m -> 0}}
>
> {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}
>
> 19
>
> This indicates 18 k values that work for any m, and one m value that works
> for any k.
>
> The suppressed error message (remove Quiet) indicates OTHER solutions may
> exist, but I think not.
>
> Bobby
>
>
> On Thu, 03 Nov 2011 03:46:30 -0500, 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}}
>>
>>
>
> --
> DrMajorBob at yahoo.com
>
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