An ODE involving delta function

x''+2x'+x=t+delta(t) x(0)=0 x'(0)=1

The textbook, "Elementary differential equations" by Edwards and Penney, gives the answer as -2+t+2exp(-t)+3t exp(-t)

It is clearly wrong, as in this case x'(0)=2, not x'(0)=1.