The goal of this problem is to solve the initial value problem
y' = -f(x)y; y(0) = 1;
where f(x) = (1 if x<=2, 3/2 if x>2):
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 dierent constant of integration. (c) Match the solutions at the points where f is discontinuous, in order to make the solution y continuous on R. Note that in this case it is impossible to make y' continuous at the points where f is discontinuous.
I just dont understand what part (c) is asking, if anyone could help me with the concepts I would really appreciate it.