How do I integrate a differential equation in MATLAB?

Question

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?

the link to the article. the equation i have used comes under Calcium Oscillations section

Answer 1

You could use Euler method to solve this problem to get a rough idea regarding the solution yet not accurate.

clear all
clc

t = 0;
dt = 0.0001;
c1 = 0.185;
c0 = 2*10^-6;
k3 = 0.1*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;

%store initial values
C(1) = c;
T(1) = t;

for i = 1:40000
    dc = ( (c1*(v1*(p_open3)+v2)*(Ca_ER)-c)- v3*( c^2 /( c^2+(k3)^2) ) );
     c = c + dt*dc;
    t  = t + dt;

    %store data
    C(i+1) = c;
    T(i+1) = t;
end

plot(T,C, 'LineWidth',2)
xlabel('time (sec)')
ylabel('c(t)')
grid on

The result is

You can also use Wolfram which gives same result.