Green's Function to Solve ODE's

Question

I'm kinda stuck on solving this ODE through using Green's function:

$$y'' + y' = f(x) , 0 < x < 1, y(0) = y'(1) = 0$$

Should I set the differential operator to $y''$ so that:

$$d^2_xG = \delta(t-t_0)?$$

I'm not quite sure where to go from here.