Help with differential equations in matlab ?

Hi , I need help with this excercise : I need to find k(speed constant ) if I know that

dx/dt=k*((a-x)^2) and I have this data :

t <min>=<0,2.5,5.6,9.6,14.6, 21.5,32.5,52.2> and

<a-x><mol/l>=<0.0050,0.0045, 0.0040, 0.0035, 0.0025,0.0020,0.0015>

I have a problem with solving an example in matlab.

<`**matlab-differential equations**`>

I´ve tried next steps:

Command W. :

t=[0 2.5 5.6 9.6 14.6 21.5 32.5 52.2];

x=[0:0.0005:0.0035];

a=0.0050;

c=a-x;

Editor ( my skript):

function dx=f(t,x)

dx=k*.((a-x).^2)

end + Run

Command W. :

tspan=0:0.0005:0.0035;

>> [x,t]=ode45(f,[0:0.0005:0.0035],0)

I don´t know how to find k

[Helena Vesteg]

And I don´t know if steps before are correct , please somebody for help it tooks me 2 days .....

Answer 1

[Sulaymon Eshkabilov]

You have confused your problem statement and its parameters. Also, there are a few errs.

(1) t=[0 2.5 5.6 9.6 14.6 21.5 32.5 52.2]; x=[0:0.0005:0.0035];

t can be set as a vector, e.g. t = linspace(0, 5, 200) or time range, e.g. t = [0, 5]

(2) Check the initial conditions, x(0) = ???. Because x(0) = 0 does not give any simulation results.

(3) check for k.

[Helena Vesteg]

does it mean that whole my matlab code is wrong ? cause I am hopeless....

[Sulaymon Eshkabilov]

No, don't think that way. We all make mistakes and learn. Learning is all about making mistakes and learn from them. Thus, try to solve it again. If you can't get it to run correctly, then you will be helped. Good luck.

[Helena Vesteg]

Thank you :) . So I changed my (code) steps like :

Comand Window:

t=[0; 2.5; 5.6; 9.6;14.6; 21.5;32.5;52.2]; I put between numbers ; cause I think it means that t is a vector

x=[0;0.0005;0.0035]; I thought that this step is corect because step is h=0.0005

Editor:

function dxdt=f(t,x) % k is unknown parameter
close all 
t_range=[0,52.2];
x0=1;
dxdt=k*((0.0050-x).^2)
end

[Helena Vesteg]

And next steps are same ....

But I still don´t know how to create matlab code for k ? I realy tried but I solved function without matlab that k is k=x/at*(a-x) (after integration and if t=0 ,x=0 ) and I know results for k but I put it only on paper I have problem with matlab cause I´ve tried too many combinations . Can you help me please to do it right and finish this excercise.