The goal of this problem is to solve the initial value problem
$y' = -f(x)y;\quad y(0) = 1;$
where $f(x)= \begin{cases} 1,&\text{if }x\leq 2\\ \frac{3}{2},& \text {if } x>2. \end{cases} $ Since $f$ is discontinuous, it is necessary to solve the above ODE separately in each of the intervals where $f$ is continuous.
(a) Determine the intervals where $f$ is continuous.
(b) Solve the equation in each of these intervals. Note that each of the solutions obtained will have a different constant of integration.
(c) Match the solutions at the points where $f$ is discontinuous, in order to make the solution $y$ continuous on $\Bbb R$. Note that in this case it is impossible to make $y'$ continuous at the points where $f$ is discontinuous.
I just don't understand what part (c) is asking, if anyone could help me with the concepts I would really appreciate it.