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proper way of posing a non-autonomous ode in mathematica?

• To: mathgroup at smc.vnet.net
• Subject: [mg100394] proper way of posing a non-autonomous ode in mathematica?
• From: sean_incali at yahoo.com
• Date: Tue, 2 Jun 2009 06:47:14 -0400 (EDT)

Hello group,

I was trying to solve a simple ODE system that has parameters that are
functions of time. Then I thought about it and I'm not sure if I'm
doing it right.

Let's say your system is

a = -k1 (t^-h) -k2 (t^-h) b
b = k1 (t) a

Then in mathematica,

a'[t] == - k1 (t ^-h) a[t] - k2 (t ^-h) b[t],
b'[t] == k1 (t ^-h) a[t]

which is solvable.

but if I pose the k1 and k2 as a function of t, like k1[t^-h] and k2
[t^-h]

Then the system becomes under-determined with 4 unknowns and 2
eqns...

So my question is how do you pose/solve a non-autonomous ode in
mathematica?

Thanks for any info in advance.

Sean