Dear ODE enthusiasts and Maple developers,

Hi everyone,

I am looking at the following ODE:

x'(t) + a(t)*x(t)  - t*a(t) + b*a(t)*f(x(t)) = 0

where x is the function of t to be found
with t>=0, x(t)>0
with initial condition x(0)=x0 > 0 given
with a(t) a known function of t inside the positive quadrant, a(t)>0
with f(x) a known function of x inside the positive quadrant, f(x)>0
with b a known positive real constant, b>0

If b=0, we have a first-order linear ODE, but I'm interested in b>0.

Hi there,

I'm struggling to understand the dynamics of a 3-D system of differential equations. I am interested in a numerical simulation. A phase diagram would be nice too. I've tried the standard bag of tricks, but remain quite lost.

Hi there,

fsolve fails me, for the first time. I have this very messy expression, which comes out of a cubic equation. It must have a zero. I plot it and the graph, smooth, shows a zero between 16.4 and 16.5, but maple's fsolve fails to find it, why's that? The slope of the function is very flat near the zero. I tried to tell maple the solution is between 16.4 and 16.5, to no avail.

Any advice will be much appreciated. The following code tells it all.

many thanks,

Patrick.