Solving the Ordinary Differential Equation

I am not sure how to solve these systems of differential equation. However, the final graph representation of the result is two exponential curves for and in respect to time.

Also, with =, the variable ks and BP are all constant.

Answer 1

[madhan ravi]

EDITED

use dsolve()

or

Alternate method using ode45:

tspan=[0 1];
y0=[0;0];
 
[t,x]=ode45(@myod,tspan,y0)
plot(t,x)
lgd=legend('Cp(t)','Cr(t)')
lgd.FontSize=20
 
function dxdt=myod(t,x) 
tau=2;
ks=3;
BP=6;
k1=5;
k2=7;
x(1)=exp(-t)/tau; %x(1)->Cp
dxdt=zeros(2,1); 
dxdt(1)=k1*x(1)-(k2/(1+BP))*x(2); %x(2)->Cr
dxdt(2)=k1*x(1)-k2*x(2);
end

[Yeahh]

So should I set these two equations as two functions and then set some values to the variables? And ended with dsolve()?

[madhan ravi]

yes declare them by using syms Ct(t) Cr(t)

and then solve them

and use fplot(Ct(t)) to plot the curve

[Yeahh]

What should I do with the constant variables?

[madhan ravi]

Substitute some numbers there

[Yeahh]

I got something like this, but when I have the t defined, it is not running and I also need to know how to display the results as a plot

syms C_T(t) C_r(t);
t=[1:10000];
equations=[diff(C_T,t)==(3*exp(-t)-(3/(1+2))*C_T), diff(C_r,t)==(3*exp(-t)-3*C_r)];
    
sol=dsolve(equations);

[Yeahh]

But the first differential equation is dcT/dt not Cp(t), is that the same?

madhan ravi's reply : no they are not the same

[madhan ravi]

dcT/dt refers to dxdt(1)

[Yeahh]

Thank you so much, I have one last question.

What doest this line means?

dxdt=zeros(2,1);

[madhan ravi]

Anytime :), It is called preallocation(please google it) imagine as a container to store something. Make sure to accept for the answer if it was helpful.