The original question is given as
$$\frac {d^3y}{dt^3}+y=u=(1-t)e^{-2t}$$
The initial value y(0) = 0 and the same for all derivatives of y.
- Determine Y(s)
- What happens to u(t) and y(t) when $t\rightarrow \infty$ ?
Through Laplace transforms and partial fractions we arrive at (also given in the answer for 1.)
$$Y(s)=\frac{1}{(s+2)^2(s^2-s+1)}$$
Now, using the final value theorem, we could evaluate
$$\lim_{t\rightarrow \infty}y(t)=\lim_{s\rightarrow 0}sY(s)$$
Using Wolfram alpha, I get
$$\lim_{s\rightarrow 0}\frac{s}{(s+2)^2(s^2-s+1)}=0$$
But the given answer to question 2. is that $|y(t)|\rightarrow \infty$ when $t\rightarrow \infty$
What am I doing wrong?