Re: Surprising DSolve problem
- To: mathgroup at smc.vnet.net
- Subject: [mg123999] Re: Surprising DSolve problem
- From: DrMajorBob <btreat1 at austin.rr.com>
- Date: Wed, 4 Jan 2012 05:05:55 -0500 (EST)
- Delivered-to: l-mathgroup@mail-archive0.wolfram.com
- References: <201201020742.CAA09063@smc.vnet.net>
- Reply-to: drmajorbob at yahoo.com
That works:
Clear[y]
y[x_] = y[x/a] /.
First@DSolve[y''[x] + (2 y[x])/(Cosh[x]^2) == 0, y, x] //
FullSimplify
y''[x] + (2 y[x])/(a^2 Cosh[x/a]^2) // Simplify
-C[2] + (C[1] + ArcTanh[Tanh[x/a]] C[2]) Tanh[x/a]
0
Bobby
On Tue, 03 Jan 2012 04:29:47 -0600, Dave Snead <dsnead6 at charter.net> wrote:
> Sam,
>
> Mathematica is deficient in this area.
> (Hopefully they'll improve this someday)
>
> Use it to solve
> y''[x] + (2 y[x])/(Cosh[x]^2) == 0
> for y and then substitute x->x/a for a solution to
> y''[x] + (2 y[x])/(a^2 Cosh[x/a]^2) == 0
>
> Cheers,
> Dave Snead
>
>
> -----Original Message-----
> From: Sam Takoy
> Sent: Sunday, January 01, 2012 11:42 PM
> To: mathgroup at smc.vnet.net
> Subject: Surprising DSolve problem
>
> Hi,
>
> I find that my Mathematica (8.0.1)
>
> can do
>
> DSolve[ y''[x] + (2 y[x])/(Cosh[x]^2) == 0, y, x]
>
> but can't do
>
> DSolve[ y''[x] + (2 y[x])/(a^2 Cosh[x/a]^2) == 0, y, x] (*Additional
> constant "a")
>
> If I am not mistaken, the equations are equivalent by a trivial change
> of variables.
>
> What's going on here?
>
> Thanks,
>
> Sam
>
>
>
--
DrMajorBob at yahoo.com
- References:
- Surprising DSolve problem
- From: Sam Takoy <sam.takoy@yahoo.com>
- Surprising DSolve problem