Solving a first order ODE using the Euler backward method (implicit)

I'm trying to solve a first order ODE with the initial condition y(5) = 0. To do this, I'm using the Euler backward method, but I'm getting these two errors:

Error using fzero (line 214)

Second argument must be finite.

Error in backwardeuler (line 22)

y(i+1) = fzero(@(Y) y(i) + dt*((2*t(i+1)-4)*exp(-Y)) - Y, y(i), options);

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% y_true = log(t^2 -4*t-4); Initial condition y(5) = 0;

% F_ty = @(t,y) (2*t-4)*exp(-y);

dt = 0.01;

t0 = 0;

tf = 3;

t = t0:dt:tf;

y(5) = 0;

% using the formula for backward euler: y(i+1) = y(i) + dt*f(y(i+1),t(i+1))

% we get

%y(i+1) = y(i) + dt*((2*t(i+1)-4)*exp(-y(i+1)));

% setting the LHS equal to zero so we can use fsolve:

% 0 = y(i) + dt*((2*t(i+1)-4)*exp(-y(i+1))) - y(i+1);

% We define y(i+1) = Y, so that

% 0 = y(i) + dt*((2*t(i+1)-4)*exp(-Y)) - Y;

options = optimset('TolX',1e-06);

for i = 1:length(t)-1

y(i+1) = fzero(@(Y) y(i) + dt*((2*t(i+1)-4)*exp(-Y)) - Y, y(i), options);

y_exact(i+1) = log((t(i+1))^2-4*t(i+1)-4);

end

figure(1)

hold on

plot(t,y,'bo')

plot(t,y_exact,'r-')

xlabel('time')

ylabel('y(t)')

title('Backward Euler method vs exact solution')

legend('Backward Euler', 'Exact')