Solve differential equation from Matlab
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Sabella Huang
on 27 May 2022
Commented: Sabella Huang
on 29 May 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
3 Comments
John D'Errico
on 27 May 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.
Accepted Answer
John D'Errico
on 27 May 2022
Edited: John D'Errico
on 27 May 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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More Answers (1)
Bjorn Gustavsson
on 27 May 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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