Backward Euler for Van der Pol equation

I'm trying to program the Backward Euler to solve Van der Pol's equation. Theoretically, this method should be stable for any step size h>0. It doesn't produce particularly stellar results, however, and my guess would be that this has to do with the inability of fsolve or the standard fixed point iteration to obtain results. Here's the code for my two attempts:

clear; clc; close all;

u0=[1;0]; %initial value
t0=0; tf=1000; %interval
N = 200; %number of points
h=(tf-t0)/(N-1); %step size
mu = 0.1; %Van der Pol parameter
f = @(t,y) vanderpoldemo(t,y,mu);
t = t0:h:tf;

u = zeros(2,N);
u(:,1)=u0;


%% attempt 1
for i = 2:N
    u(:,i)=rand(1,2);
    for times = 1:2
    u(:,i) = u(:,i-1)+h*f(t(i-1),u(:,i));
    end
end

plot(t,u(1,:))

%% attempt 2
for i = 2:N
    u(:,i) = fsolve(@(U) u(:,i-1)+h*f(t(i-1),U)-U,rand(1,2), options);
end

I'm quite frustrated by this and would greatly appreciate any help.