Answer
See details below.
Work Step by Step
The general solution of $y'=-2 y+8 =-2(y-4)$ is
$$y=4+c e^{-2t}.$$
When $y(0)=3$, then $3=4+c$, i.e. $c=3-4=-1$. In this case
$$y=4- e^{-2t}.$$
When $y(0)=4$, then $4=4+c$, i.e. $c=0$. In this case
$$y=4.$$
See the graphs below.
![](https://gradesaver.s3.amazonaws.com/uploads/solution/9e60aef8-c315-4407-8290-62e0c026d20c/steps_image/small_1575116861.png?X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAJVAXHCSURVZEX5QQ%2F20240727%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240727T015447Z&X-Amz-Expires=900&X-Amz-SignedHeaders=host&X-Amz-Signature=a337fd58670f9dd2142af9e1bc0d1514b4b287ea5fcb6f0f8b710da24b4e5bc7)