DSolve algorithm

*To*: mathgroup at smc.vnet.net*Subject*: [mg18987] DSolve algorithm*From*: "Atul Sharma" <atulksharma at yahoo.com>*Date*: Tue, 3 Aug 1999 13:44:34 -0400*Sender*: owner-wri-mathgroup at wolfram.com

I most certainly do not want to come across as a Mathematica basher. The truth is that I used Mathematica as a student and continue to use it despite annoying pressure from Information Services to join the site license program which they have with another program. Having said that, I am a bit perplexed by the difference noted below and wonder if DSolve can be augmented to allow it to deal with the problem: I have a system of differential equations representing a multicompartment pharmacokinetic model of dialysis and impaired kidney function. By tedious algebra, I can approximate this system with a second order differential equation with time varying coefficients, describing what happens in the blood compartment. If I make some inspired variable substitutions, I can get the equation in the following reduced form: -a y[x] -qf (-g +x) y'[x] +qf^2 x vi y''[x] ==gu In this form, Mathematica can generate a solution in terms of Kummer functions. No solution is forthcoming with either the original variables, the original system, or earlier steps in the road to the Kummer differential equation. This itself doesn't bother me, though I do have a number of variants of this basic problem that I also would like to solve. What provoked this question was what happened when I asked the other system dsolve command to solve the same problem. The reduced equation above returns a solution in terms of Whittaker functions equivalent to Mathematica's solution. However, I had never bothered to try the unreduced equation and only realized yesterday that another system gives me a solution with the unreduced equation and even with the original system of equations. I obviously realize that generalizing from n=1 is dangerous at the best of times, and this certainly isn't enough to make me want to switch from a platfrom with which I'm very comfortable. However, I do have a number of variants of this system that I'm working with and need to solve, and I wonder if Mathematica DSolve can be made smarter or if v 4.0 has a 'new, improved' DSolve functionality. I also confess to some curiousity as to why this would be the case. Any comments would be appreciated, as I would like to understand this difference. Atul -------------------------------------------- Atul Sharma MD, FRCP(C) Pediatric Nephrologist, McGill University/Montreal Children's Hospital email: mdsa at musica.mcgill.ca