matlab code:

clear

$\%$

$\%$ Initial data

num$\_$y$(1,1)=$ input$("$Input initial condition y$1\_0=")$;

num$\_$y$(1,2)=$ input$("$Input initial condition y$2\_0=")$;

$\%$ Time interval $[$ti$,$tf$]$

ti $=$ input$("$initial time $=")$;

tf $=$ input$("$final time $=")$;

nt $=$ input$("$number of time steps $=")$;

dt$=($tf$-$ti$)/$nt;

$\%$ Input matrix A for the $2$x$2$ system dy$/$dt $=$ A y

A$(1,1)=$ input$("$matrix coefficient A$11=")$;

A$(1,2)=$ input$("$matrix coefficient A$12=")$;

A$(2,1)=$ input$("$matrix coefficient A$21=")$;

A$(2,2)=$ input$("$matrix coefficient A$22=")$;

disp$("$Display matrix eigenvalues"$)$

eig$($A$)$

B$=$ eye$(2)+$ dt $*$ A;

x$(1)=$ti;

for i$=2$:nt$+1,$

num$\_$y$($i$,1$:$2)=$ num$\_$y$($i$-1,1$:$2)*$ B$$;

x$($i$)=$ti$+($i$-1)*$dt;

end

subplot$(211),$ plot$($x$,$num$\_$y$($:$,1)),...\%$ indicates line continuation

title$($y$1($t$)),$xlabel$($t$),$grid,...

subplot$(212),$plot$($x$,$num$\_$y$($:$,2)),...$

title$($y$2($t$)),$xlabel$($t$),$grid