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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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