Start with the characteristic equation r^(3)-3r^(2)+3r-1=0 Factor the constant. -1=(1*-1). First try r=1 (1)^(3)-3(1)^(2)+3(1)-1=0 True statement, so r-1=0 is a factor Rearrange the terms so it's easier to take out the known factor. r^(3)-r^(2)-2r^(2)+2r+r-1=0 Factor out the (r-1) term r^(2)(r-1)-2r(r-1)+(r-1)=0 (r-1)(r^(2)-2r+1)=0 Factor the binomial (r-1)((r-1)(r-1))=0 (r-1)(r-1)(r-1)=0 Triple root, multiply by t for each repeat Result: Y=c_(1)e^(t)+c_(2)te^(t)+c_(3)t^(2)e^(t)