Find the solution $of$ the given initial value problem.

$y^{(4)}-y=u_1(t)-u_2(t),y(0)=17,y^{\text{'}}(0)=18,y^{\text{'}\text{'}}(0)=7,y^{\text{'}\text{'}\text{'}}(0)=-6$

$y(t)=u_{2}h(t-1)-u_{1}h(t-2)+5cost+12sint+12e^{-t}+36e^t$

where $h(t)=-1+\frac{1}{2}cost+\frac{1}{4}{e}^{-t}+\frac{1}{4}{e}^t$

$y(t)=u_{1}h(t-1)-u_{2}h(t-2)+5cost+12sint+9e^{-t}+3e^t$

where $h(t)=-1+\frac{1}{2}cost+\frac{1}{4}{e}^{-t}+\frac{1}{4}{e}^t$

$y(t)=u_{1}h(t-1)-u_{2}h(t-2)+5cost+12sint+3e^{-t}+9e^t$

where $h(t)=-1+\frac{1}{2}cost+\frac{1}{4}{e}^{-t}+\frac{1}{4}{e}^t$

$y(t)=u_{1}h(t)-u_{2}h(t)+10cost+24sint+12e^{-t}+36e^t$

where $h(t)=-1+\frac{1}{2}cost+\frac{1}{4}{e}^{-t}+\frac{1}{4}{e}^t$

$y(t)=u_{1}h(t-1)-u_{2}h(t-2)+10cost+24sint+3e^{-t}+9e^t$

where $h(t)=-1+\frac{1}{2}cost+\frac{1}{4}{e}^{-t}+\frac{1}{4}{e}^t$