Stochastic Analysis - Reading 1

Today I made the plot of
x' = -y, x0 = x
y' = -(y-x)/epsilon, y0 = y

which, by what the paper states, leads to the following equation for x in the limit as epsilon -> 0:
x' = -x, x0 = x

in Matlab, using analycal tool, such as solve the equation for x, y analytically, then let epsilon approaching zero, in the hope that x_epsilon -> x, and the solution curve (x_epsilon, y) converges to (x,y) but no hope... dunno why.

Next step will be, using numerical tool.