Consider the initial value problem 4y" + 12y' + 9y = 0, y(0) = a, y'(0) = -1. Find the critical value of a that separates solutions that become negative from those that are always positive for t > 0....

Please help me with this problem I have posted multiple times and received multiple wrong answers from them, so I request you if you don't know correctly to solve it then please don't solve it.

I NEED ONLY CORRECT ANSWERS...

0. NOTE: Enter an exact answer. a = "/>
Extracted text: Consider the initial value problem 4y" + 12y' + 9y = 0, y(0) = a, y'(0) = -1. Find the critical value of a that separates solutions that become negative from those that are always positive for t > 0. NOTE: Enter an exact answer. a =