You're homogeneous solution is x = Ae^(-t)cos(t) +Be^(-t)*sin(t)
How did you go about trying to find the particular solution?
If you use undetermined coefficients
xp = Cte^(-t)cos(t) +Dte^(-t)*sin(t) you have to multiply by t since
e^(-t)*sin(t) and e^(-t)*cos(t) are homogeneous solutions
If you use variation of parameters W = e^(-2*t)
you obtain z1' = -sin(t)^2 z2 ' = sin(t)cos(t)