1. The problem statement, all variables and given/known data For the equation y=-4e^t -4/3-2t+Ce^(3t/2), find the initial value y(0)=y_0 that separates solutions that grow positively as t -> infinity from those that grow negatively. 2. Relevant equations (All are given in the problem statement.) 3. The attempt at a solution I have half a large page scribbled in small writing over this. I attempted things like Ce^(3t/2) >= 4e^t+2t, which made a pretty graph on Wolfram-alpha. However, the closest I got was this: since t=0, the only thing that can vary in the equation is C. y_0=-4-0-4/3+C. C=y_o+16/3. Sadly, however, this seems to be utterly useless. The answer is -16/3. How would one come to this answer? Thanks.