$y_1^{\text{'}}=6y_1+8y_2+3e^{-2x}$

$y_2^{\text{'}}=3y_1+y_2-5e^{-2x}$

In my attempt in using MATLAB to solve for the general solution of ODE as shown and particular solution if y$(0)=1$ of the question as shown in the picuture. The following are my codings:

$\%$ Define the system

function dxdt $=$ system$($x$,$ t$)$

x$1=$ x$(1)$;

x$2=$ x$(2)$;

dxdt $=[6*$x$1+8*$x$2+3*$exp$(-2*$t$)$; $3*$x$1+$ x$2-5*$exp$(-2*$t$)]$;

end

$\%$ Define the initial conditions

x$0=[1$; $0]$;

$\%$ Define the time points

t $=0$:$0\mathrm{.}1$:$10$;

$\%$ Solve the system

$[$t$,$ x$]=$ ode$45($@system, t$,$ x$0)$;

$\%$ Plot the solution

plot$($t$,$ x$($:$,1),\text{'}$b$\text{'},$ t$,$ x$($:$,2),\text{'}$r$\text{'})$;

xlabel$(\text{'}$Time$\text{'})$;

ylabel$(\text{'}$x$1$ and x$2\text{'})$;

legend$(\text{'}$x$1\text{'},\text{'}$x$2\text{'})$;

However, it outputs errors as shown below, i don't know where did i do wrong. Please correct and teach me$.$

Index exceeds the number of array elements. Index must not exceed $1.$

Error in ODE$\_$Q$3>$system $($line $4)$

x$2=$ x$(2)$;

Error in odearguments $($line $92)$

f$0=$ ode$($t$0,$y$0,$args$\{$:$\})$; $\%$ ODE$15$I sets args$\{1\}$ to yp$0.$

Error in ode$45($line $104)$

odearguments$($odeIsFuncHandle$,$odeTreatAsMFile, solver$\_$name, ode, tspan, y$0,$ options, varargin$)$;

Error in ODE$\_$Q$3($line $15)$

$[$t$,$ x$]=$ ode$45($@system, t$,$ x$0)$;