Solve differential equation from Matlab

Question

Sabella Huang 2022-5-27

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https://ww2.mathworks.cn/matlabcentral/answers/1728265-solve-differential-equation-from-matlab

评论： Sabella Huang 2022-5-29

采纳的回答： John D'Errico

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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Sabella Huang 2022-5-27

Hello, thx for your suggestions. I want to solve this just symbolically

John D'Errico 2022-5-27

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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Answer 1

John D'Errico 2022-5-27

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https://ww2.mathworks.cn/matlabcentral/answers/1728265-solve-differential-equation-from-matlab#answer_972710

编辑：John D'Errico 2022-5-27

在 MATLAB Online 中打开

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))

ans =

Where W0 is the Lambert W function. Actually, the zero'th branch thereof, so lambertw(0,u).

help lambertw
 LAMBERTW Lambert's W function.
    W = LAMBERTW(Z) solves W*exp(W) = Z.
    W = LAMBERTW(K,Z) is the K-th branch of this multi-valued function.
 
    References:
    [1] Robert M. Corless, G. H. Gonnet, D. E. G. Hare,
    D. J. Jeffrey, and D. E. Knuth, "On the Lambert W Function",
    Advances in Computational Mathematics, volume 5, 1996, pp. 329-359.
 
    [2] Corless, Jeffrey, Knuth, "A Sequence of Series
    for The Lambert W Function", ISSAC '97

    Documentation for lambertw
       doc lambertw

    Other functions named lambertw

       sym/lambertw

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Walter Roberson 2022-5-27

note that is two different solutions

Sabella Huang 2022-5-29

ok this work... thx

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Answer 2

Bjorn Gustavsson 2022-5-27

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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1728265-solve-differential-equation-from-matlab#answer_972720

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