3 materials - composite wall , 1D transient heat convection and conduction

hello, i have the next problem, left side convection and right side adiabadic (i know only left side conditions)

I am a heat transfer engineer so i know how to solve in analytically but im trinig to solve this transient problem by numerical methods, with ode func or with runge kutta

i wrote the matrix but i dont know what to do next:

clc;
%3 materials - composite wall , 1D transient heat convection and conduction

rho_1=7833;%[kg/m^3]
rho_2=1409;%[kg/m^3]
rho_3=1470;%[kg/m^3]

c_p_1=434.667;%[J/kg/C]
c_p_2=1350;%[J/kg/C]
c_p_3=827.256;%[J/kg/C]

h_inf=200;

k_1=41.0987;%[W/m/C]
k_2=0.3941;%[W/m/C]
k_3=0.4;%[W/m/C]

h=100;%[W/m^2/C]
L_1=1E-3;%[m]
L_2=5E-3;%[m]
L_3=5E-3;%[m]

A_11=(-1/rho_1*c_p_1*L_1)*(((1/h_inf+L_1/2*k_1)^-1)+((1/h+L_1/2*k_1+L_2/2*k_2)^-1));
A_12=(-1/rho_1*c_p_1*L_1)*(((1/h+L_1/2*k_1+L_2/2*k_2)^-1));
A_13=0;

A_21=(1/rho_2*c_p_2*L_2)*(((1/h+L_1/2*k_1+L_2/2*k_2)^-1));
A_22=(-1/rho_2*c_p_2*L_2)*(((1/h+L_1/2*k_1+L_2/2*k_2)^-1)+((1/h+L_3/2*k_3+L_2/2*k_2)^-1));
A_23=(1/rho_2*c_p_2*L_2)*(((1/h+L_3/2*k_3+L_2/2*k_2)^-1));

A_31=0;
A_32=(1/rho_3*c_p_3*L_3)*(((1/h+L_3/2*k_3+L_2/2*k_2)^-1));
A_33=(-1/rho_3*c_p_3*L_3)*(((1/h+L_3/2*k_3+L_2/2*k_2)^-1));

A=[A_11 A_12 A_13;A_21 A_22 A_23;A_31 A_32 A_33];
t=180;%[sec] transient time
dt=0.01;%[sec] step time
T_inf=50;%[C]
C=[(1/rho_1*c_p_1*L_1)*(T_inf/(1/h_inf+L_1/2*k_1)) 0 0]';

syms T_1 T_2 T_3
T_t=[T_1 T_2 T_3]';
dT_dt=A.*T_t+C;