system of differential equations mathematica help

*To*: mathgroup at smc.vnet.net*Subject*: [mg129366] system of differential equations mathematica help*From*: 01af <alicerferrier at gmail.com>*Date*: Mon, 7 Jan 2013 23:07:41 -0500 (EST)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com*Delivered-to*: l-mathgroup@wolfram.com*Delivered-to*: mathgroup-newout@smc.vnet.net*Delivered-to*: mathgroup-newsend@smc.vnet.net

Before anyone starts to type: I have read the top post on a similar matter, but the reply makes no sense to me so if anyone can give my issue a read through I would be grateful. Thanks. ok I am modelling airflow in the upper airway for application i obstructive sleep apnoea, but I have hit a brick wall with mathematica. I have a system of 3 differential equations with boundary conditions, and I need to solve to find 3 unknown functions numerically so that they may be plotted in various graphs. The equations are as follows: D[a[x]*u[x], x] == 0, u[x] u'[x] == -p'[x], p[x] - 1 == 2 (1 - ((a[x])^(-3/2))) - 50 (a''[x]). with boundary conditions: u[0] == 0.1, a[0] == 1, a[10] == 1, p[10] == 1. so initially I tried to use NDSolve like so.. Code: NDSolve[{D[a[x]*u[x], x] == 0, u[x] u'[x] == -p'[x], p[x] - 1 == 2 (1 - ((a[x])^(-3/2))) - 50 (a''[x]), u[0] == 0.1, a[0] == 1, a[10] == 1, p[10] == 1}, {a}, {x, 0, 10}] but mathematica does this: Code: Power::infy: "Infinite expression 1/0.^(3/2) encountered. " Infinity::indet: Indeterminate expression 0. ComplexInfinity encountered. >> Infinity::indet: Indeterminate expression 0. ComplexInfinity encountered. >> General::stop: Further output of Infinity::indet will be suppressed during this calculation. >> NDSolve::ndnum: Encountered non-numerical value for a derivative at x == 0.`. >> which is super annoying, any pointers as to where I'm going wrong would be great. I'm not even sure if I should be using NDSolve so let me know what you think. thanks in advance a.

**Follow-Ups**:**Re: system of differential equations mathematica help***From:*Oliver Ruebenkoenig <ruebenko@wolfram.com>