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MathGroup Archive 2002

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Re: DSolve solution validation

  • To: mathgroup at smc.vnet.net
  • Subject: [mg33941] Re: DSolve solution validation
  • From: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>
  • Date: Wed, 24 Apr 2002 01:21:48 -0400 (EDT)
  • Organization: Universitaet Leipzig
  • References: <aa3fm7$7pl$1@smc.vnet.net>
  • Reply-to: kuska at informatik.uni-leipzig.de
  • Sender: owner-wri-mathgroup at wolfram.com

Hi,

this result is nonsense

Try

DSolve[y'[z]==Sqrt[y[z]^2],y[z],z]

DSolve[] expect *continuos* right hand sides and a function
involving Abs[] is not continuous.

Regards
  Jens


Regards
  Jens

Vladimir Bondarenko wrote:
> 
> Sometimes, it is easy to double check the DSolve's output.
> 
> However, an attempt to solve
> 
>                              DSolve[y'[z] == Abs[y[z]], y[z], z]
> yields
> 
> {{y[z] -> InverseFunction[(-(Log[2*Sqrt[Im[K$3541]^2 + Re[K$3541]^2] +
> (2*(-Im[K$3541]^2 + Im[K$3541]*Im[#1] - Re[K$3541]^2 + Re[K$3541]*Re[#1]))/
> Sqrt[Im[K$3541]^2 - 2*Im[K$3541]*Im[#1] + Im[#1]^2 + Re[K$3541]^2 -
> 2*Re[K$3541]*Re[#1] + Re[#1]^2]]/Sqrt[Im[K$3541]^2 - 2*Im[K$3541]*Im[#1] +
> Im[#1]^2 + Re[K$3541]^2 - 2*Re[K$3541]*Re[#1] + Re[#1]^2]) + Log[2*Sqrt[Im[#1]^2 +
> Re[#1]^2] + (2*((-Im[K$3541])*Im[#1] + Im[#1]^2 - Re[K$3541]*Re[#1] + Re[#1]^2))/
> Sqrt[Im[K$3541]^2 - 2*Im[K$3541]*Im[#1] + Im[#1]^2 + Re[K$3541]^2 -
> 2*Re[K$3541]*Re[#1] + Re[#1]^2]]/Sqrt[Im[K$3541]^2 - 2*Im[K$3541]*Im[#1] +Im[#1]^2 +
> Re[K$3541]^2 - 2*Re[K$3541]*Re[#1] + Re[#1]^2])*(-K$3541 + #1) & ][z + C[1]]}}
> 
> If I try to use D[] to check it, I get an expression with ByteCount of
> 737608. The attempt to Simplify this huge expression for the derivative
> gave no answer after 1 hour at CPU = Athlon FX 1600+ / RAM = 512 Mb.
> 
> Question # 1:   Is the above shown solution correct? (It involves 2 free constants,
>                 K$3541 and C[1], but after simplification K$3541 might disappear?
>                 (Also, this ODE is not linear, so the answer to it might have 2 free
>                 constants?)
> 
> By hand I found
> 
>                 z Sign[y[z]] - Log[y[z]] = C[1]
> 
> Question # 2:   Is this implicit solution correct? (I am not 100% sure)
> 
> Question # 3:   Looks like I've calculated a collection of ODEs about which
>                 I suspect that the corresponding DSolve's solutions are invalid.
>                 What are the possible ways to double check these solutions?
>                 Any modules written in Mathematica? Anything else?
> 
> Vladimir Bondarenko


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