differential equation

[CdeMills]

Hello,

I'm trying to simulate an electrical circuit whose time-domain differential
equation is
V" + k1 V' +k2 V = a1 I' + a2 I
Vs(t) - Rs I = V
where V and I are the device voltage and current, respectively, and the rest
are constants. Vs is the time-varying voltage source, and Rs its internal
resistance. Starting from equilibrium, all values and their derivatives are
set to zero. 

I don't see how to formulate the problem, in particular adding the source
equation into the picture. 

LSODE: let's say x1 = V, x2 = I, x3 = V'; so we have
x1' = x3
x2' = ??? => I' depends on Vs'(t) ???
x3' = a1 * ??? + a2 x2 - k1 x3 - k2 x1
How to fill the "???"

DASSL: same variables
res1 = x1'-x3
res2 = ...
res3 = x3' - a1 x2' - a2 x2 - k1 x3 - k2 x1
In all cases, I need a relationship around I', and would like Vs(t) to be a
step source, in this case Vs'(t) would become infinite ???

Any hints ?

Regards

Pascal 




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