MATLAB: How to solve this system using ODE45

codeMATLABodeode45

The ODE system
dx/dt = -8/3 x + yz;
dy/dt = -10y + 10z;
dz/dt = -x*y + 28y – z when t=[0,50]
I only learned how to solve one equation each but,
I wanna solve this system using ODE45 on matlab
please help me how to make the script.

Best Answer

You first must assign ‘x’, ‘y’, and ‘z’ to a vector, then create the appropriate first-order differential equations with respect to each variable.
Example:
% % % MAPPING:  x = v(1),  y = v(2),  z = v(3)
% dv(1,:) = -8/3.*v(1) + v(2).*v(3);
% dv(2,:) = -10*v(2) + 10*v(3);
% dv(3,:) = -v(1).*v(2) + 28*v(2) - v(3);
v_fcn = @(t,v) [-8/3.*v(1) + v(2).*v(3);  -10*v(2) + 10*v(3);  -v(1).*v(2) + 28*v(2) - v(3)];
ts = [0  50];
init_cond = [10; 10; 10];
[T,V] = ode45(v_fcn, ts, init_cond);
figure(1)
plot(T,V)
grid
I used an anonymous function here, simply for convenience. See the section on ‘Anonymous Functions’ in Function Basics for details on how to write them and use them.
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