Answer each of the questions on your own paper. Be sure to show your work so that partial credit can be adequately assessed. Credit will not be given for answers (even correct ones) without supporting work. Put your name on each page of your paper. A short table of laplace transforms and a table of common exact values of trigonometric functions is included on page 2: [16 points each] solve each of the following initial value problems. Be sure to show all of your work. (a) y + t y. = 0, y(1) = 3 (b) y 2y = 2e5t + 5e2t, (c) y : [18 points] y = 6t4, A solution containing 0. 5 pounds of salt per gallon enters the tank at a rate of 6 gallons per minute. A drain is opened at the bottom of the tank through which the well stirred solution leaves the tank at the same rate of 6 gallons per minute.
