I need help solving the following set of differential equations. This MUST be done in MATLAB. I can solve them otherwise, but I am struggling to accomplish this using MATLAB.

$${dX_c \over dt} = v_x \cos(\theta) - v_y \sin(\theta)$$$${dY_c \over dt} = v_x \sin(\theta) + v_y \cos(\theta)$$$${d \theta \over dt} = \omega_z$$ $${d v_x \over dt} = {1 \over m} \left [ F_x + mv_y \omega_z \right] $$ $${d v_y \over dt} = {1 \over m} \left [ F_y - m v_x \omega_z \right] $$ $${d \omega_z \over dt} = {1 \over I_z} T_{ext} $$

Question

I need help solving the following set of differential equations. This MUST be done in MATLAB. I can solve them otherwise, but I am struggling to accomplish this using MATLAB. 

$${dX_c \over dt} = v_x \cos(\theta) - v_y \sin(\theta)$$$${dY_c \over dt} = v_x \sin(\theta) + v_y \cos(\theta)$$$${d \theta \over dt} = \omega_z$$ $${d v_x \over dt} = {1 \over m} \left [ F_x + mv_y \omega_z \right] $$ $${d v_y \over dt} = {1 \over m} \left [ F_y - m v_x \omega_z \right] $$ $${d \omega_z \over dt} = {1 \over I_z} T_{ext} $$

anonymous · Answer

The initial conditions are as follows: $X_c(0) = 0 ; ~ Y_c(0) = 0; ~ \theta(0) = 0;~ v_x(0) = 0;~ v_y(0) = 0;~ \omega_z(0) = 0$
The force and external torque have the following definition: $$F_x(t) = 1000 \cos(0.1 t) ; ~ F_y = 100 \sin(0.2 t); ~ T_{ext} = 50(1 + \sin(0.3t))$$Finally, $m = 100~ {\rm and} ~ I_z = 1000$