[laplace transforms for solving differential equations] this is the heart of the post-midterm 2 material. here, i give you a number of examples. in a couple of parts, i intentionally make you deal with some "special" cases (e. g. a coefficient that come out to be zero) so that you know how to handle those. (a) for the differential equation: y' + 5y = e-4u(t), y(0) = 2 i. find the laplace transform y(s) of y(t). ii. mark the pole locations of y(s) in the complex frequency (s) plane. iii. take the inverse laplace transform of y(s) to obtain y(t) for t > 0.