How do I solve this differential system by using ode45?

Here is my system. how do i use ode45 to solve this. I dont know how to build a array contain all these funciton and put into ode45.

Thank for helping me.

x' = 6*x/y;
y' = x'*4;
z' = 16*x';
x0   %Initial condition are known, 
y0
z0

Answer 1

[Sam Chak]

Hi @Gan Huang

Since is known, you can make direct substitutions into and . Here is the demo:

function Demo_ode45

close all

clc

tspan = [0 1]; % time span of simulation

y0 = [1 0.5 0.25]; % initial values

[t, y] = ode45(@(t, y) odefcn(t, y), tspan, y0);

plot(t, y, 'linewidth', 1.5)

grid on

xlabel('Time, t [sec]')

ylabel('x, y, z')

title('Time responses of the system')

legend('x', 'y', 'z', 'location', 'best')

end

function dydt = odefcn(t, y) % Ordinary Differenctial Equations

dydt = zeros(3,1);

dydt(1) = 6*y(1)/y(2);

dydt(2) = 4*(6*y(1)/y(2));

dydt(3) = 16*(6*y(1)/y(2));

end

Result: