Find a continuous solution of the initial-value problem where (y' = g(t)), (g(t) = begincases 2, & t > 0 0, & t ≤ 0 endcases), (y(0) = 0).

a) (y(t) = 2t) for (t > 0), (y(t) = 0) for (t ≤ 0)
b) (y(t) = 0) for (t > 0), (y(t) = 0) for (t ≤ 0)
c) (y(t) = 2) for (t > 0), (y(t) = 0) for (t ≤ 0)
d) (y(t) = 2t) for all (t)