Re: Simplifying a second order eq. system tests=PRIORITY_NO_NAME version=2.55

*To*: mathgroup at smc.vnet.net*Subject*: [mg45967] Re: [mg45928] Simplifying a second order eq. system tests=PRIORITY_NO_NAME version=2.55*From*: Andrzej Kozlowski <akoz at mimuw.edu.pl>*Date*: Sat, 31 Jan 2004 05:20:30 -0500 (EST)*References*: <200401300915.EAA04894@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

On 30 Jan 2004, at 10:15, Gunnar Lindenblatt wrote: > Hi, > > I just switched from another system to Mathematica > 5. While all "complicated" operations (like importing Wave-Files, > filtering, > parameter fitting, plotting) just work fine, I still have problems > with the > "basics" like solving or even simplifying equations: > > For example, to get the telegraph equation by self-induction and > capacitive > coupling: > > (One can solve this problem on the space of a postage stamp...) > > In[1] := Remove["Global`*"] > > In[2] := myEqn1 = -Dt[u,x] == r i + l Dt[i,t] > > In[3] := myEqn2 = -Dt[i,x] == s u + c Dt[u,t] > > > > Direct approach: Using "Solve" > > In[4] := Solve[{myEqn1,myEqn2}, {Dt[u,{x,2}]}] > > results an empty set of solutions: > > {{}} > > > > Second try: Using "Reduce" > > In[5] := Reduce[{myEqn1,myEqn2}, {Dt[u,{x,2}]}] > > results: > > Reduce::nsmet: This system cannot be solved with the methods available > to > Reduce. > > Third try: Using "Eliminate" > > In[6] := Eliminate[{myEqn1,myEqn2}, {Dt[i,x],Dt[i,t]}] > > results: > > True > > That's fine! However, it does not really help me... > > > > (By the way, the result should be: > > Dt[u,{x,2}]== r s u + (r c + l s) Dt[u,t] + l c Dt[u,{t,2}]) > > Any ideas? -- Perhaps this problem is too simple for Mathematica, so it > rejects any help ;-) > > - Gunnar > > Solve, Reduce, Eliminate etc are all algebraic functions so they are obviously not going to do any differentiating for you. Secondly, how is Mathematica to know what in your equations is a variable and what is a constant? The current version still can't read human minds. Now, if you remember all these points than your problem becomes as trivial with Mathematica as it is without it: Step 1. This tells Mathemaitca your constants: SetAttributes[r, Constant]; SetAttributes[l, Constant]; SetAttributes[c, Constant]; SetAttributes[s, Constant]; Step 2. Setting up your equations: myEqn1 = -Dt[u, x] == r*i + l*Dt[i, t]; myEqn2 = -Dt[i, x] == s*u + c*Dt[u, t]; Step 3. Solving your problem: Eliminate[{Dt[myEqn1, x], myEqn2, Dt[myEqn2, t]}, {Dt[i, x], Dt[i, t], Dt[i, t, x]}] Dt[u, {x, 2}] == r*s*u + c*r*Dt[u, t] + l*s*Dt[u, t] + c*l*Dt[u, {t, 2}] Andrzej Kozlowski Chiba, Japan http://www.mimuw.edu.pl/~akoz/

**References**:**Simplifying a second order eq. system tests=PRIORITY_NO_NAME version=2.55***From:*"Gunnar Lindenblatt" <Gunnar.Lindenblatt@pobox.com>