First Order Differential Equation

*To*: mathgroup at smc.vnet.net*Subject*: [mg23819] First Order Differential Equation*From*: "Atul Sharma" <atulksharma at yahoo.com>*Date*: Sat, 10 Jun 2000 03:00:28 -0400 (EDT)*Organization*: McGill University*Sender*: owner-wri-mathgroup at wolfram.com

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