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 $2\frac{dy}{dt}-y=5\cos t$.
Use this solution to determine a 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 $y(t)=c e^{t/2}+2\sin t -\cos t$, see WolframAlpha. This function $y(t)$ goes to $\infty$ when $c>0$, to $-\infty$ when $0>c$ and oscillates when $c=0$. The value $c=0$ corresponds to the initial value $y(0)=2\sin 0-\cos 0=-1$, so $a=-1$ is the answer. One more?