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Re: Mathematica won't solve simple diff. eqn.--Correction
*To*: mathgroup at smc.vnet.net
*Subject*: [mg24753] Re: Mathematica won't solve simple diff. eqn.--Correction
*From*: "Christopher R. Carlen" <crcarle at sandia.gov>
*Date*: Wed, 9 Aug 2000 02:32:14 -0400 (EDT)
*Organization*: Sandia National Laboratories
*References*: <8mdlt6$5jt@smc.vnet.net>
*Sender*: owner-wri-mathgroup at wolfram.com
I made a mistake in my original article, the relevant portion of which
is:
"Christopher R. Carlen" wrote:
>
> 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.
> 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)
The solutions shown are to the inhomogeneous system:
-4 i1'[t] + 8 i2'[t] - 25 i1[t] + 20 i2[t] == -80 + 720 E^(-5 t)
-4 i1'[t] + 8 i2'[t] - 10 i1[t] + 40 i2[t] == 640 E^(-5 t)
When I do:
In:
DSolve[{-4 i1'[t] + 8 i2'[t] - 25 i1[t] + 20 i2[t] == -80 + 720 E^(-5
t),
-4 i1'[t] + 8 i2'[t] - 10 i1[t] + 40 i2[t] == 640 E^(-5 t)}, {i1, i2},
t ]
Mathematica 4.0 simply outputs the DSolve statement with no result.
When I do:
In:
i1 = 4 + 64 Exp[-5 t] - 68 Exp[-4 t]
i2 = 1 - 52 Exp[-5t] + 51 Exp[-4 t]
Simplify[ -4 D[i1, t] + 8 D[i2, t] - 25 i1 + 20 i2 == -80 + 720 Exp[-5
t] ]
Simplify[ -4 D[i1, t] + 8 D[i2, t] - 10 i1 + 40 i2 == 640 Exp[-5 t] ]
Out:
true
true
indicates that the solutions are valid.
The question is then:
Why can't Mathematica solve the system?
_______________________
Christopher R. Carlen
Sr. Laser/Optical Tech.
Sandia National Labs
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