How to solve this system using ODE45?

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.

Answer 1

[Star Strider]

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.

Answer 2

[Sameer kumar nayak]

7d²x/dt²+3dx/dt+5x+6=0 how can we solve using matlab using ode45??

[Steven Lord]

See the "Nonstiff van der Pol Equation" example on this documentation page. You should be able to use the same techniques as that example to solve your ODE.