Re: Manipulating differential equations

*To*: mathgroup at smc.vnet.net*Subject*: [mg18583] Re: [mg18552] Manipulating differential equations*From*: "Carl K.Woll" <carlw at fermi.phys.washington.edu>*Date*: Tue, 13 Jul 1999 01:01:22 -0400*Organization*: Department of Physics*References*: <199907100618.CAA02980@smc.vnet.net.>*Sender*: owner-wri-mathgroup at wolfram.com

Martin, Here are two ideas. 1. Use pure functions: dg1/.c->(Exp[-a #]&) 2 a a g ---- - ---- a x a x E E 2. Define c to be your test function, evaluate dg1, and then clear c. A nice way to do this is to use Block: Block[{c}, c[x_]:=Exp[-a x]; dg1] 2 a a g ---- - ---- a x a x E E As for what goes wrong with your attempt, look at the FullForm of c'[x]. FullForm[c'[x]] Derivative[1][c][x] As you can see, c[x] does not appear in the FullForm of c'[x]. Hence, when you apply your replacement rule, nothing happens to c'[x]. Carl Woll Dept of Physics U of Washington Martin Heimann wrote: > Dear colleagues, > > I would like to insert test functions into an expression that contains > differentials: > > dg1 = c''[x] + g c'[x] > > I would like e.g. to replace c[x] by Exp[-a x]: > > dg1/.c[x]->Exp[-a x] > > but this doesn't work; one has to put substitution rules for each of the > derivatives explicitly. Is there a more elegant way to achieve this? > > Cheers, > Martin Heimann > ------------------------------------------------------------------ > Max-Planck-Institut fuer Biogeochemie > Postfach 100164, D-07701 Jena, Germany > (Street Address: Tatzendpromenade 1a) > > Tel.: +49-3641-64-3773/3701, Fax.: +49-3641-64-3710 > Email: martin.heimann at bgc-jena.mpg.de

**References**:**Manipulating differential equations***From:*Martin Heimann <martin.heimann@bgc-jena.mpg.de>