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Re: Mathematica won't solve simple diff. eqn.--Correction


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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