solving a set of differential equations with ode45

Hello everyone, 

I am trying to solve the set differential equations (see in code) with ode 45 but I suppose that i haven't declared my function properly. Does anyone have an idea on the way to fix this problem... I get this message of error...

%% Initiate the script 
clc; clear; close all
% yy = 1-2*xx+3*xx.^2;

% %% Check the stored value of the selected point
% [x1 y1]
%% Question 3
%initial conditions 
xx = linspace(0,10,1e3).';
IC1=[0; 0; 298; 298];
opts= odeset('RelTol',1e-8,'AbsTol',1e-10);
[tout,Xout] = ode45(@(t,x)mydyn(t,x),xx,IC1,opts);

%% Function definition
function dx = mydyn(t,x)
% Define the parameters 
Ct= 200;                %[J/K]
ht=140;                 %[W/m^2K]
At=0.02;                %[m^2]
he=200;                 %[W/m^2K]
Ae=pi;                  %[m^2]
Te= 298;                %[K]
V=6*pi;                 %[m^3]
rho=1;                  %[kg/m^3]
cp=4200;                %[J/kgK]
J=300;                  %[kgm^2]
c=2;                    %[Nms]
c3=0.1;                 %[Nms^3]
cq=0.09;                %[Ws^4]
M=[5,15,25,55]; 

T=x(1);
Tt=x(2);
theta=x(3);
thetadot=x(4);

%state model
dT=(V*rho*cp)^-1*(he*Ae(Te-T)+ht*At*(Tt-T)+cq*thetadot^4);
dTt=(ht*At)*(Ct)^-1.*(T-Tt);
dtheta=thetadot;
dthetadot=(M-c*thetadot-c3*thetadot^3)./J;

dx=[dT,dTt,dtheta,dthetadot]';
end

Error in Ryelandt_288861_Assignment2>@(t,x)mydyn(t,x)

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 Ryelandt_288861_Assignment2 (line 32)

[tout,Xout] = ode45(@(t,x)mydyn(t,x),xx,IC1,opts);

Answer 1

[James Tursa]

Initial conditions is a 4-element vector:

IC1=[0; 0; 298; 298];

But in your derivative function you have this:

M=[5,15,25,55]; % 4-element vector
    :
dthetadot=(M-c*thetadot-c3*thetadot^3)./J; % 4-element vector
dx=[dT,dTt,dtheta,dthetadot]'; % 4-element vector in that last spot

So dx ends up being 7 elements instead of 4, hence the mismatch error.

[Guillaume Ryelandt]

Thank you, I Managed to correct the mistake!