The characteristic equation is r^{2}+ 2r + 17 = 0

The roots of characteristic equation are : -1± 4i

Then the general solution of homogeneous equation is :.........(i)

Then \(\displaystyle{y}'{\left({0}\right)}=-{c}{1}{e}-{t}{\cos{{4}}}{t}-{4}{c}{1}{e}-{t}{\sin{{4}}}{t}-{c}{2}{e}-{t}{\sin{{4}}}{t}-{4}{c}{2}{e}-{t}{\cos{{4}}}{t}\) .......(ii)

Using initial values in (i) and (ii), find c1 and c2 and then write the general solution.

The roots of characteristic equation are : -1± 4i

Then the general solution of homogeneous equation is :.........(i)

Then \(\displaystyle{y}'{\left({0}\right)}=-{c}{1}{e}-{t}{\cos{{4}}}{t}-{4}{c}{1}{e}-{t}{\sin{{4}}}{t}-{c}{2}{e}-{t}{\sin{{4}}}{t}-{4}{c}{2}{e}-{t}{\cos{{4}}}{t}\) .......(ii)

Using initial values in (i) and (ii), find c1 and c2 and then write the general solution.