Matlab-ode45 vs Octave-lsode for a nonlinear ODE

[Torquil Macdonald Sørensen]

Hi, I'm getting very different results when solving the following 
initial value ODE problem in Matlab and Octave:

dy/dt=1/sqrt(y^2 + 1)+y-y^2  on  t \in [0,10] with y(0) = 0

 From looking at the equation, I believe that the Matlab solution is the 
correct one, so I'm wondering if I have not converted the Matlab-file 
correctly to Octave? Or does the Octave algorithm not work in this 
situation? It does not change when I lower the values for the absolute 
and relative tolerances with lsode_options, so maybe I have done 
something wrong and I'm solving a different ODE in Octave.

Here are the Octave and Matlab programs that I thought were solving the 
same equation:


*** Octave version ***

function nonlinear_de

% Time span
t = linspace(0,10,100);

% Initial condition
y0=[0];

% Solve the DE
lsode_options('absolute tolerance', 0.0001);
[y, istate, msg] = lsode("ode",y0,t);

istate
msg

% Plot the solution
plot(t,y(:,1),'-')

% Differential equation
function dydt = ode(t,y)
dydt = [ 1/sqrt(y(1)^2 + 1)+y(1)-y(1)^2];


*** Matlab version ***

function nonlinear_de

% Time span
tspan=[0 10];

% Initial condition
y0=[0];

% Solve the DE
[t,y] = ode45(@ode,tspan,y0);

% Plot the solution
plot(t,y(:,1),'-')

% Differential equation
function dydt = ode(t,y)
dydt = [ 1/sqrt(y(1)^2 + 1)+y(1)-y(1)^2];