Backward Euler - part 2

The figure below shows the solution to the ODE from Curtiss & Hirschfelder, previously presented here. The figure below, however, was solved using the Backward Euler's method. The Backward Euler clearly has better convergence and stability compared to the Forward Euler. Irrespective of the step size 'h', the solutions clearly converge. The increase in calculation time from the iteration at each time step is made up for by the superior stability characteristics of this method.



So, which of the above solutions is now the "correct" one?!