Just passing by to thank to everyone for the help.
The problem has been just solved.

Kind regards.
restart;
f := t -> sum(Dirac(t - t0), t0 = 1 .. 10);
s := dsolve(diff(v(t), t) = f(t) - v(t)/alpha);
Y := rhs(s);
c__1 := 2;
plot([eval(Y, alpha = 0.15)], t = 0 .. 4, color = [red], labels = ["Gas release after each rumen secondary contraction (min)", "Rumen headspace volume (L)"], labeldirections = ["horizontal", "vertical"]);

Hi Tom,

Thanks for your time figuring out this. No, this is not what I want.

I actually want that something like this. With a kind of a maximum volume the gas can be produced and a minimum residue, such that the gas volume inside the container is stable.

Hello, again!

I adapted the commands you taught me on this thread, and it worked really well for my problem (I am modeling gas volume in a digestor in which a certain volume of gas escapes automatically every 3 minutes, but then the volume increases again becasue it is continually produced...).

However, I noticed that in the long run the volume of gas increases (Figure), and I was wondering if there is a way to set a maxmum value and a minimum value such that the oscilations stay inside those boundaries.

You could set any arbitrary maximum constraint (Vmax) and a minimum constraint (Vmin) so that the gas volume stay between the parameters below:

restart;
with(inttrans);
f := t -> sum(Dirac(t - a), a = 1 .. 10);
s := dsolve(diff(v(t), t) = alpha*v(t) - f(t), v(t), method = laplace);
Y := rhs(s);
v(0) := 30;
alpha := 0.036;
plot(Y, t = 0 .. 10, labels = ["SCC", "V(L)"]);

Thanks a million!

Thank you very much!!!

The answers posted here are what I was looking for.

I appreciate your help and comments.

Kind regards,

Andre

Hi,

Thanks for your comments.

To clarify, I am trying to understand how to plot the follwing ODE in orther to solve a different problem:

db/dt = 𝑓(𝑡) − ∝*b(t),

Where 𝑏(𝑡)= amount of drug in the bloodstream at time t ;

𝑓(𝑡)= dosing pattern of injections at time t (This is a discrete value since dosages will remain constant);

∝ = metabolism of the drug.

When the ODE is solved, the final equation becomessomething like this:

𝑏(𝑡) = 𝑏(0)*𝑒xp (−∝𝑡) + 𝑢(𝑡 − 𝑎₁ )*𝑒xp (−∝(𝑡−𝑎₁ )) + 𝑢(𝑡 − 𝑎₂ )*𝑒xp (−∝(𝑡−𝑎₂ )) + ⋯ + 𝑢(𝑡 − 𝑎_n )*𝑒xp (−∝(𝑡−𝑎_𝑛))

b(0) = 1;
∝ = 0.023;
𝑎_{𝑛 = 1...10 (number of injections).}

How could this equation be plotted in Maple to observe the spikes in the drug concentration in the bloostream after every injection? I mean, as time goes on, the function is turned on and off, and the graph is expected to show temporarys spike in the drug concentrations followed by the decays according to the multiple injections.

Thanks for your help.

Hi guys,

Thanks for the help.

I appreciated.