Answer:
k=18, general solution does not exist.
Step-by-step explanation:
If f(t)=y=e3t is a solution to the differential equation
d2ydt2−9dydt+ky=0,
then
y = e^(3t)
y' = dy/dt = 3y
y'' = d2ydt2 = 9y
y'' - 9y' + ky = 0
9y - 9(3y) + ky = 0
(9-27+k)y = 0
solve for y
(9-27+k) = 0
k = 18
general solution is when y=e^(3t)=0, or t-> -infinity
