# Problem with matrix differential equation resolve in Matlab with ode45

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Antoine W on 26 Apr 2021
Commented: James Tursa on 26 Apr 2021
Hi,
I would like to solve this linearized matrix differential equation: My program has no errors but the result it gives seems inconsistent. Here is my program:
vt= linspace(0,10,500);
v=0.5*vt;
Q0=[0 0;0 0];
tspan=[0 10];
M=[80.8 2.32;2.32 0.28];
K0=[-80.95 -2.6;-2.6 -0.8];
K2=[0 76.6 ; 0 2.65];
C1=[0 33.87; -0.86 1.68];
q=ones(2,2);
[tSol,QSol]=ode45(@(tSol,QSol) myodefun(tSol,q,vt,v,M,K0,K2,C1,f),tspan,Q0);
function dQdt=myodefun(t,q,vt,v,M,K0,K2,C1)
v=interp1(vt,v,t);
Q1=q(:,1);
Q2=q(:,2);
dQ1dt=M*Q2;
dQ2dt=-v*C1*Q2-(9.81*K0+v*v*K2)*Q1;
dQdt=[dQ1dt;dQ2dt];
end
Do you see anything I did wrong to solve this equation?

James Tursa on 26 Apr 2021
Edited: James Tursa on 26 Apr 2021
Normally I would have expected ode45( ) to pass q as a 4x1 column vector. Also, I don't see anything in your code solving for qdotdot that would involve backslash or the inverse of M. E.g., something like this for a derivative function:
% assume q is passed in as 4x1 column vector
function dQdt=myodefun(t,q,vt,v,M,K0,K2,C1)
v=interp1(vt,v,t);
qdot = q(3:4);
q = q(1:2);
qdotdot = M \ (-v*C1*qdot - (9.81*K0+v*v*K2)*q);
dQdt=[qdot;qdotdot];
end
And what is f? I don't see that defined. And I don't see it being used in myodefun.
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James Tursa on 26 Apr 2021