This question is similar to 2.1: 13-15 and 20, 21.
Work out your answer on paper or using appropriate software. Then put your answer into Webex Poll.
Find the general solution of the differential equation $3\frac{dy}{dt}-y= 5e^{-t}$. Determine the number $a$ such that for the initial value $y(0)=a$ the transition from one type of behaviour to another occurs.
Put the number $a$ as your answer into DE-Poll (Use fractions or two decimals if needed)
The general solution is $y(t)=C e^{t/3}-\frac54 e^{-t}$, see WolframAlpha. This function goes to $\infty$ when $c>0$, and goes to $-\infty$ when $0>c$. It goes to $0$ when $c=0$. The value $c=0$ is where the transition occurs, and it corresponds to the initial value $y(0)=-5/4$. So $a=-5/4$ is the answer. One more?