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Re: First Order Differential Equation

• To: mathgroup at smc.vnet.net
• Subject: [mg23876] Re: [mg23819] First Order Differential Equation
• From: "Richard Finley" <rfinley at medicine.umsmed.edu>
• Date: Thu, 15 Jun 2000 00:51:13 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

Atul,

Well it is obviously easy to solve the ODE formally using the usual integrating factors, but the question is can you do integrals of the form:
Integrate[p[t],t] 
since the integrating factors involve such terms.  The answer would appear to be no for your equations in all their generality.  

regards...RF

>>> "Atul Sharma" <atulksharma at yahoo.com> 06/10/00 01:00AM >>>
Looking at this first-order differential equation, I am embarrassed to admit
how much time I've spent trying to figure out an approach that can yield a
closed form solution. It is a much simplified version of a more complicated
model, which we usually solve by numeric integration, and I had hoped to
illustrate how the simple version could still yield qualitative insights.
However, perhaps I'm missing something obvious, but I can't seem to get it
into a solvable form.

For what it's worth, the time constant k in the exponential is << 1 in
non-dimensional units. All the coefficients are constants.

p[t]*y[t] + y'[t] == q[t]

p[t_] = (A1 + A2/E^(k*t))/(A3 - a1/E^(k*t) - a2*t)
q[t_] = -((Cb*(A4 + A5/E^(k*t)))/(A3 - a1/E^(k*t) - a2*t))

With apologies if it's trivial and thanks for any suggestions.

A. Sharma

--
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Atul Sharma MD, FRCP(C)
Pediatric Nephrologist,
McGill University/Montreal Children's Hospital