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Re: Manipulating differential equations
*To*: mathgroup at smc.vnet.net
*Subject*: [mg18617] Re: [mg18552] Manipulating differential equations
*From*: "Wolf, Hartmut" <hwolf at debis.com>
*Date*: Tue, 13 Jul 1999 01:01:37 -0400
*Organization*: debis Systemhaus
*References*: <199907100618.CAA02980@smc.vnet.net.>
*Sender*: owner-wri-mathgroup at wolfram.com
Hello Martin,
Martin Heimann schrieb:
>
> 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?
>
you have to substitute the _function_ :
In[16]:= dg1 = c''[x] + g c'[x]//FullForm
Out[16]//FullForm=
Plus[Times[g,Derivative[1][c][x]],Derivative[2][c][x]]
In[17]:= dg1/. c->(Exp[-a #]&)
Out[17]//FullForm=
Plus[Times[Power[a,2],Power[E,Times[-1,a,x]]],
Times[-1,a,Power[E,Times[-1,a,x]],g]]
(of course you normally don't define dg1 wrapped in FullForm)
Alternatively you could also localize the function c[x] to Exp[-a x]:
In[18]:= Block[{c},c[x_]:=Exp[-a x];dg1]
Out[18]//FullForm=
Plus[Times[Power[a,2],Power[E,Times[-1,a,x]]],
Times[-1,a,Power[E,Times[-1,a,x]],g]]
---your's hw
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