Consider the initial value problem ( ty" + (2t + 6) y' + (t + 6) y=0 (* y(1 ) = 2 and y'(1) = 6 e e Given that y, (t) = er is a solution of the differential equation, solve the initial value problem (*) y (t ) Your answer should be a function of t.To Find the general solution y (+ ) = Get+ cz. Given initial conditions 4 (1 ) = 2 and y' (1) = b substitute in (oct ) + = 4 y (1 ) = C,6 + 2 for y'll), first find y' (+ ) y ' ( 1 ) = - Ge - ( 2 is substitute $ = 1 - Ge - SC + 9, 5 - solveing both equation c, and ' 6218 sothe solutionis y ( + ) = 18 - t 8