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MathGroup Archive 2000

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Re: Mathematica won't solve simple diff. eqn. system

  • To: mathgroup at smc.vnet.net
  • Subject: [mg24755] Re: [mg24699] Mathematica won't solve simple diff. eqn. system
  • From: "Richard Finley" <rfinley at medicine.umsmed.edu>
  • Date: Wed, 9 Aug 2000 02:32:19 -0400 (EDT)
  • Sender: owner-wri-mathgroup at wolfram.com

Christopher,
There is a problem with your solution...it is not a solution.  If you substitute your solution into the original equations you get:
{-80 + 720* E^-5*t, 640*E^-5*t} rather than the required {0,0}

There is a solution to the equations, namely 
i1[t]=0
i2[t] = 0

regards,  RF


>>> "Christopher R. Carlen" <crcarle at sandia.gov> 08/03/00 11:19PM >>>
Mathematica 4.0 and linear constant coefficient differential equations:

I have the following system:

-4 i1'[t] + 8 i2'[t] - 25 i1[t] + 20 i2[t] == 0
-4 i1'[t] + 8 i2'[t] - 10 i1[t] + 40 i2[t] == 0
i1[0]==0
i2[0]==0

Which when I try to solve with DSolve, it fails.  

It seems any system of the form:

y1'[t] + y2'[t] + C1 y1[t] + C2 y2[t] == 0
y1'[t] + y2'[t] + C3 y1[t] + C4 y2[t] == 0

can't be solved.  If the coefficients on y1' and y2' are not the same
between the two equations, then it can be solved.

The problem is that there is a solution to the above system, which I
have verified.  That solution is:

i1[t_] = 4 + 64 E^(-5 t) - 68 E^(-4 t)
i2[t_] = 1 - 52 E^(-5 t) + 51 E^(-4 t)

So the question is:  If there is a solution (and not a very difficult
one) why can't Mathematica find it???  Is there some way to coerce Mathematica to
produce the equation, in both the symbolic and numerical situations?

These types of systems arise frequently in the study of electronic
circuits.  Numerical solvers like SPICE solve them without any
difficulty.  I have struggled with getting Mathematica to solve them for a long
time.  Sometimes I force a numerical solution by perturbing the
coefficients a bit, as long as the error is acceptible.  

But I would like to understand better what the hangup is.  I have had a
diff. eqns. course, but haven't gone into systems yet. 

Thanks.
-- 
_______________________
Christopher R. Carlen
Sr. Laser/Optical Tech.
Sandia National Labs




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