Solve differential equation from Matlab
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Sabella Huang
le 27 Mai 2022
Commenté : Sabella Huang
le 29 Mai 2022
Hello guys,
I want to ask about, how to solve the differential equation in MATLAB for the equation:
dx/dt = (ka*C(xmax-x)-kd*x)/(1+ka*x)
thx
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John D'Errico
le 27 Mai 2022
Are ka and kd constants, or is k separate from a and d, so there are three unknown constants. Is xmax known? Is it a value that x may not exceed? Is C a function? Or is C just a known constant?
When you are too vague, you make it impossible for people to help you.
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John D'Errico
le 27 Mai 2022
Modifié(e) : John D'Errico
le 27 Mai 2022
Making various assumptions, we see the solution as:
syms ka kd C xmax
syms x(t)
dsolve(diff(x) == (ka*C*(xmax-x)-kd*x)/(1+ka*x))
Where W0 is the Lambert W function. Actually, the zero'th branch thereof, so lambertw(0,u).
help lambertw
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Bjorn Gustavsson
le 27 Mai 2022
For a numerical integration of this ODE look at the help and documentation for ode45 and its siblings, also look at the examples and demos related to these ODE-solvers, you find these in odeexamples. That is perhaps the best way to get started (maybe it will not make you an expert in DE in general, but it will get you going.) You can also read the code of the different demos and adapt them to suit your problem.
For an analytical solution you might have success with dsolve from the symbolic toolbox if you have access to that.
HTH
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