Please solve & show steps... 0 is a parameter.Solve the initial value problem.9.u(t) = u9/2 (1)h(t– ) -U13/2 (t)h(t –)where h(t) = k – ke-8 sin-13.V636363t – ke-t/8-co-8638u(t) = [u9/2...

Please solve & show steps...

0 is a parameter. Solve the initial value problem. 9. u(t) = u9/2 (1)h(t – ) - U13/2 (t)h(t –)where h(t) = k – ke-8 sin- 13. V63 63 63 t – ke-t/8 -co- 8 63 8 u(t) = [u9/2 (t) – u13/2 (t)]h(t) where h(t) = k – ke-8 V63 sin- t – ke 63 V63 -cos 8 -t/8 63 u(t) = u9/2 (t)h(t –-) – u13/2(1)h(t 13. where h(t) 2 V63 co- -t + ke' 8 (63 -t/8 -sin- 63 V63 - = ke -t/8 u(t) = u9/2 (1)h(t – 9. ) – u13/2 (1)h(t –- 13. V63 V63 -sin- 63 where h(t) = k – ke 2 V63 -t/8 cos -t – ke -1/8 u(t) = [u9/2 (t) – u13/2(t)]h(t) where h(t) = k – ke V63 t - ke¬t/8 V63 -sin- V63 -t/8 co- V63 8 63 8 "/>
Extracted text: A certain spring-mass system satisfies the initial value problem. u" +u' + u = kg(t), u(0) = 0,4'(0) = 0 where g(t) = ug2 (t) – u 13/2 (t) and k > 0 is a parameter. Solve the initial value problem. 9. u(t) = u9/2 (1)h(t – ) - U13/2 (t)h(t –)where h(t) = k – ke-8 sin- 13. V63 63 63 t – ke-t/8 -co- 8 63 8 u(t) = [u9/2 (t) – u13/2 (t)]h(t) where h(t) = k – ke-8 V63 sin- t – ke 63 V63 -cos 8 -t/8 63 u(t) = u9/2 (t)h(t –-) – u13/2(1)h(t 13. where h(t) 2 V63 co- -t + ke' 8 (63 -t/8 -sin- 63 V63 - = ke -t/8 u(t) = u9/2 (1)h(t – 9. ) – u13/2 (1)h(t –- 13. V63 V63 -sin- 63 where h(t) = k – ke 2 V63 -t/8 cos -t – ke -1/8 u(t) = [u9/2 (t) – u13/2(t)]h(t) where h(t) = k – ke V63 t - ke¬t/8 V63 -sin- V63 -t/8 co- V63 8 63 8