How do I integrate a differential equation?

Hi, I want to integrate a differential equation dc/dt. Below is the code and the values of the variables.

clear all;
c1=.185;c0=2*10^-6;k3=.1*10^-6;
v1=6;v2=.11;v3=.09*10^-6;
Ca_ER=10*10^-6;Ca_cyto=1.7*10^-6;
p_open3=0.15;c=15*10^-6;
dcdt= (c1*(v1*(p_open3)+v2)*(Ca_ER)-c)-v3*((c)^2)/(c^2+(k3)^2);

I know there is an integral function but I am not sure how to apply for this equation. How do I proceed from here? Please help. The value of initial c, if needed, can be taken as 0.15*10^-6. Also, I need to plot the obtained result versus time. So will get an array of values or just a single value?

Answer 1

[Star Strider]

Try this:

c1=.185;c0=2E-6;k3=1E-7;
v1=6;v2=.11;v3=9E-8;
Ca_ER=10E-6;Ca_cyto=1.7E-6;
p_open3=0.15;

ci=15E-6;
dcdt = @(t,c) (c1.*(v1.*(p_open3)+v2).*(Ca_ER)-c)-v3.*((c).^2)./(c.^2+(k3).^2);
tspan = linspace(0, 10, 25);
[t,c] = ode45(dcdt, tspan, ci);

figure(1)
plot(t, c)
grid

See the documentation for ode45 and Anonymous Functions for details.

[nashyshan]

Thank you @star . But I have already tried this.

[John D'Errico]

Then explain why that solution was not acceptable.

[nashyshan]

@john D'Errico. I am supposed to obtain periodic oscillations, but am not able to do so. since I wasn't familiar with the ODE functions in MATLAB I though I was doing something wrong. But I think it has to do with the equations.

[Walter Roberson]

Use Star Strider's code but increase the upper time bound. For example,

tspan = linspace(0, 40, 75);

I do not understand why the wiggles are not visible if an upper time bound of 30 is used, but they are visible if 35 is used and clearly peak near 20.