How to solve 2nd order coupled ODE in Matlab using ode45 -or likewise function ?

I have to solve 2nd order coupled ODE for z(t) and x(t) in the equations below where all other terms are known and the derivatives are with respect to 't'

1. (m) z''(t) + b z'(t) + c z(t) = 0
2. (I+A) x''(t) + B x'(t) + c x(t) z(t) =0

The first equation is uncoupled and I was successful in finding out z(t) by solving the first equation alone using ode45(), but I am not able to solve both the equations combined.

Answer 1

[Mischa Kim]

Mahesh, it works just the same way. Something like:

[t,XSol] = ode45(@myODE, tspan, X0)
...

function Xd = myODE(t,X)

% define matrices and constants

x  = X(1);
xd = X(2);
z  = X(3);
zd = X(4);

Xd = [ xd;...
       (-B*xd - c*x*z)/(I + A);...
       zd;...
       (-b*zd - c*z)/m];
end

The initial conditions, X0, need to be set accordingly, of course.

[Ryan Compton]

Hi, I am trying to implement this code using my own diff EQs but I am getting errors. Here is my code

function Xd = myODE(t,X)

k1 = 5000   
m1 = 300
k2 = 400000000
m2 = 10
r = 0
b = 3000

x1 = X(1)
x1d = X(2)
x2 = X(3)
x2d = X(4)

Xd = [x1d;...
    (-k2/m1)*x2) + (k2/-m1)*x1 - (-b/m1)*x2d + (b/-m1)*x1d + (k1/-m1)*x1 - (k1/-m1)*r;...
    x2d;...
    (-k2/m2)*x2) + (k2/m2)*x1 - (b/m2)*x2d + (b/m2)*x1d]

end

and then calling:

tspan = [0 15]
X0 = [0 0 0 0]

[t,XSol] = ode45(@myODE, tspan, X0)
plot(t,XSol(:,1))

I am getting the following errors:

Error in odearguments (line 90)
f0 = feval(ode,t0,y0,args{:});   % ODE15I sets args{1} to yp0.

Error in ode45 (line 115)
  odearguments(FcnHandlesUsed, solver_name, ode, tspan, y0, options, varargin);

Error in Untitled5 (line 4)
[t,X] = ode45(@fun, tspan, X0)

Would you be able to help me understand the issue. i am using matlab 2018a.