Use methods of undetermined coefficients to find one solution of:
y'' + 2y' +2y =
First the homogenous solution. The charac. equation is r^2+2r+2=0 which gives us:
r= -1+i and r= -1-i, then yh= c1exp(-t)cos(t)+ c2exp(-t)sin(t).
Now in this case the guess for the particular solution is yp= (at+b)exp(-t)cos(t)+ ...
A 2nd order ODE is solved. The solution is detailed.