use laplace transformation to solve $y^{(4)}-16y=0$, being $y(0)=1$, $y'(0)=0$, $y''(0)=0$, $y'''(0)=0$

Question

Folowing the process, I came to $$Y=\frac{s^3}{s^4-16}$$

However, when trying to write the fraction as a sum of other fractions,the system is undetermined.

$$\frac{s^3}{s^4-16}=\frac{A}{(s-2)}+\frac{B}{(s+2)}+\frac{Cs+D}{(s^2+4)}$$

What am I doing wrong?

Thanks!