Using ODE 45 coupled ODEs

Hi!

I am supposed to solve these two linear ODEs

k = 0.0440;
C_A0 = 0.3045;
epsilon = 2;
alpha = 0.001;
F_A0 = 2.5;
rho = 0.001;

ode1 = diff(y) == -(alpha/2*y)*(1+epsilon*X)*rho;
ode2 = diff(X) == k*C_A0*(1-X)/(F_A0*1+epsilon*X)*y*rho;

I cant figure out how to use ode45 but i have tried something like this by using some other answers which i dont understand..

function dz = myode2(v,z)
syms v z
alpha = 0.001;
C0 = 0.3;
esp = 2;
k = 0.044;
f0 = 2.5;
dz = zeros(2,1);
dz(1) = k*C0/f0*(1-z(1)).*z(2)./(1-esp*z(1));
dz(2) = -alpha*(1+esp*z(1))./(2*z(2));
ode45(@myode2,[0 500],[0 1])
end

This does not work tho..

Anyone knows how to solve this by ode45?

Answer 1

[Star Strider]

Start with what you already have:

syms X(t) y(t) Y 
k = 0.0440;
C_A0 = 0.3045;
epsilon = 2;
alpha = 0.001;
F_A0 = 2.5;
rho = 0.001;
ode1 = diff(y) == -(alpha/2*y)*(1+epsilon*X)*rho;
ode2 = diff(X) == k*C_A0*(1-X)/(F_A0*1+epsilon*X)*y*rho;

then use odeToVectorField and matlabFunction (linked to in that doeumentation) to create your ODE anonymous function.

This appears to be a homework assignment, so I leave the rest to you.