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