1.

Entered Answer Preview Result (s^2)+49-7*5-3 $2 + 49 -7s - 3 incorrect S s/[(s^ 2)+49] $2 + 49 correct 2 + (7s + 3) ($2 +49) [2+(7*s+3)*[(s^2)+49]1/([(s^ 2)+49]^2) incorrect (82 + 49) 2 3 t* sin(7*t) +7*cos(7*t)+(3/7)*sin(7*t) t sin(7t) + 7 cos(7t) + - sin(7t) incorrect At least one of the answers above is NOT correct.Consider the initial value problem Y +49y =cos(7t), y(0)=7, y'(0)=3. a. Take the Laplace transform of both sides of the given differential equation to create the corresponding algebraic equation. Denote the Laplace transform of y() by Y (s). Do not move any terms from one side of the equation to the other (until you get to part (b) below). g ' {52+49) 753 ':| 2o Nelp (formulas) 49 b. Solve your equation for '(s). + s+ .,5'2 | Y(s) = {u()} = W c. Take the inverse Laplace transform of both sides of the previous equation to solve for y(t). y(t) =| rsin(7) +Teos(7t) + 2 sin(7r) At least one of the answers above is NOT correct. Find the Laplace transform of the periodic function f(t) whose graph is given below. - - 1 0 -1 (Click on graph to enlarge) 1 4 F(s) = [{f(t) } = + 1 - e te dt (4-t)e dt o 2 = help (formulas)Entered Answer Preview 1 1/(1-[e^(4*s)1) 1 - e4s t*[e^(-s*t)]*dt te-stat (4-t) * [en (-s*t )]*dt (4 - t)e- stat 1/(s^2) At least one of the answers above is NOT correct.Transform the differential equation 7y" + 70y" - 343y' - 3430y = 7e-it y(0) = 0 y' (0) = 0 y"(0) = 1 into an algebraic equation by taking the Laplace transform of each side. Use Y for the Laplace transform of y, (not Y(s)). Therefore Y 5+ 7 Taking the inverse Laplace transform we get y =\f\f