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

• To: mathgroup at smc.vnet.net
• Subject: [mg100433] Re: proper way of posing a non-autonomous ode in mathematica?
• From: dh <dh at metrohm.com>
• Date: Wed, 3 Jun 2009 05:28:37 -0400 (EDT)
• References: <h02vor$8fi$1@smc.vnet.net>

Hi Sean,

see below, Daniel



sean_incali at yahoo.com wrote:

> 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]

here k1 and k2 seem to be known

> 

> 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...

now, k1 and k2 seem to be unknown functions. Therefore, you need 2 more 

equations.



> 

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

> mathematica?

> 

> Thanks for any info in advance.

> 

> Sean

> 

> 

> 

> 

>