\fHelp me with this Clos Let's solve a similar problem step-by-step to understand the concepts better. Find y as a function of t if 16y" - 64y' + 89y = 0, y(1) = 2, y'(1) = 2. y = Here's a step-by-step solution guide. Step 1 It is helpful to notice that if u(t) = y(t + 1), then u satisfies the same differential equation as y, and the initial conditions are u(0) = 2 and u'(0) = 2. Can you use the auxiliary equation to find the general solution for u? Step 2 The auxiliary equation is 1672 - 64r + 89 = 0, which has the roots r = 2 + i. The general solution for u is u = et (ci cos ($t) + c2sin (t)). Can you use the initial conditions to find c, and c2?Step 3 The derivative of the solution is u' = 2e2t (c1 cos (it) + c2sin (t)) + et (-$cisin ($t) + $c2cos (5t)) The initial conditions lead to the equations 2 = C1 2 = 2city and the solution is (C1, c2) = (2, -8). The solution of the initial value problem for u is u(t) = et (2 cos (it) - $ sin (it)), and the solution for y(t) = u(t - 1) is y(t) = e2(t-1) (2 cos ( $(t - 1)) - $ sin ( (t - 1))).Find y as a function of t if 121y" - 66y' + 18y = 0, y(5) = 1, y'(5) = 7. 11 (1-5 ) y= e COS 3 (t- 5 ) 11 sin 3 11 + 95 11 (t- 5 )