For $0<a<1$, directly solve the IVP: $$f''(x) - 3f'(x) + 2f(x) = k\delta(x-a)$$ $$f(0) = f'(0) = 1$$
Where $\delta$ is the dirac delta function and $k$ is a real number.
I can attain the complementary function easily, and get $Ae^x + Be^{2x}$ for arbitrary $A$ and $B$, but I'm having difficulties with finding the particular integral.