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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



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