1. (40 points) Solve the following differential equation problems. Keep 3 decimals. Show your work clearly. a. = -0.1y(t) + 200, given y(0) = 100. Calculate y(15). b. y = -0.1y(t) + 200t, given y(0) = 50. Calculate y(5). c. y = 0.1y(t) + 200e0.02t, given y(0) = 10. Calculate y(3). d. y = -0.1y(t) + 200, given y(5) = 7. Calculate y(10). Hint: You may need to revise the formulas (2) and (3) in Page 3 of "E428_Last Topic..." lecture notes in d21 content.