Using dsolve gives the incorrect solution unless you force it to use Laplace transforms. 

Notice that Y5 is the correct solution, not the Y coming from dsolve.

DE17:=diff(y(t),t$2)+y(t)=Dirac(t-Pi)+Dirac(t-2*Pi)+Dirac(t-3*Pi);
Y:=dsolve({DE17,y(0)=0,D(y)(0)=0},y(t));
plot(rhs(Y),t=0..6*Pi);
with(inttrans):
Y2:=laplace(DE17,t,s);
Y3:=solve(Y2,laplace(y(t),t,s));
Y4:=subs({y(0)=0,D(y)(0)=0},Y3);
Y5:=invlaplace(Y4,s,t);
plot(Y5,t=0..6*Pi);
 

Anybody run into this problem before?