Convert the given initial value problem into an initial prob

Convert the given initial value problem into an initial problem for the system

y⁽⁵⁾(t) - y⁽²⁾(t) +8y(t) = cos(y(t)) y(0)1, y\"(0)=0, y⁽³⁾(0)=2, y⁽⁴⁾(0) = 1

Solution

Let y\'\'=v then y^(5)=v\'\'\'

now the system is y\'\' = v ;y(0)=1

                        v\'\'\'-v+8y=cos(y) ; v(0)=0, v\'(0)=2, v\'\'(0)=1