Answer
See the details below.
Work Step by Step
The general solution of $y'=2(y-10)$ is
$$y=10+c e^{2t}.$$
When $y(0)=25$, then $25=10+c$, i.e. $c=25-10=15$. In this case
$$y=10+15 e^{2t}.$$
When $y(0)=5$, then $5=10+c$, i.e. $c=5-10=-5$. In this case
$$y=10-5 e^{2t}.$$
See the graphs below.
