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