Solve:

y(4)+8y+16y=0\displaystyle {y}^{{{\left({4}\right)}}}+{8}{y}{''}+{16}{y}={0}

y(0)=2,y(0)=2,y(0)=8,y(0)=24\displaystyle {y}{\left({0}\right)}=-{2},\quad{y}'{\left({0}\right)}={2},\quad{y}{''}{\left({0}\right)}=-{8},\quad{y}{'''}{\left({0}\right)}={24}