Now that we have figured out how to do step 1, we are going to try and do steps 1 and 2. Given the differential equation y" + 3y' + 5y = 0, y(0) = - 2, y'(0) = 1 Apply the Laplace Transform and solve for Y(s) = L{y} Y(s) = To solve an initial value problem using the Laplace transform takes three steps. 1. Take the Laplace transform of both sides of your ODE. This transforms your ODE into an ALGEBRAIC equation! 2. Solve the resulting algebraic equation for Y(s) 3. Take the inverse Laplace transform. Your result is the solution, y(t).

9 23

7 20 21

A King in ancient times agreed to reward the inventor of chess with one grain of wheat on the first of the 64 squares of a chessboard. On the second square, the King would place two grains of​ wheat, on the third​ square, four grains of​ wheat, and on the fourth square eight grains of wheat. If the amount of wheat is doubled in this way on each of the remaining​ squares, how many grains of wheat should be placed on a square 16​? Also, find the total number of grains of wheat on the board at this time and their total weight in pounds.​ (Assume that each grain of wheat weighs​ 1/7000 pounds.)

5. Find AB ?