Solve system of differential equations

I am facing problem in solving the differential equation

is a vector () as shown in code and is also a vector (). x11=[x1,y1]. I want to solve , where represents derivative with respect to time. Can any one help me to find out x11 vs time. (Note and x11 are the same.) (Preferably use fsolve as I tried using it).

close all
clear all
clc
x01=-5;y01=-7;
x0=[x01,y01]';
beta=25;

syms x1 y1 t
x11=[x1,y1]';

c1=(1/2)*(x1-i*sin(t))^2+(3/2)*(y1-i*cos(t))^2;
row=100*exp(0.1*t);
g1=y1-x1-cos(t);
L1=c1-(1/row)*log(1-row*g1);
grad1 = gradient(L1,x11');
hess1 = hessian(L1,x11');
phi1=-(hess1)^(-1)*(grad1+diff(grad1,t));
u1=-beta*(hess1)^(-1)*x11+phi1

u1 = 

[Torsten]

u1 is a 2x2 matrix, x11 is a 2x1 vector.

What do you mean by

x11dot = u1

?

Maybe you mean

x11dot = u1*x1

?

[Yokuna]

Thanks for pointing out, I have corrected the question.

Answer 1

[Torsten]

x01=-5;y01=-7;
x0=[x01,y01]';
beta=25;
syms x1 y1 t
x11=[x1,y1]';
c1=(1/2)*(x1-i*sin(t))^2+(3/2)*(y1-i*cos(t))^2;
row=100*exp(0.1*t);
g1=y1-x1-cos(t);
L1=c1-(1/row)*log(1-row*g1);
grad1 = gradient(L1,x11');
hess1 = hessian(L1,x11');
phi1=-(hess1)^(-1)*(grad1+diff(grad1,t));
u1=-beta*(hess1)^(-1)*x11+phi1
fun = matlabFunction(u1,'Vars',{t,x1,y1})
fun = @(t,y)fun(t,x1,y1);
y0 = [x01,y01];
tspan = [0 1]
[T,Y] = ode45(fun,tspan,y0)
plot(T,[real(Y),imag(Y)])

[Yokuna]

It gives error solving it through ode45, as the inputs needs to be floats.

[Torsten]

Replace

fun = @(t,y)fun(t,x1,y1);

by

fun = @(t,y)fun(t,y(1),y(2));