Problem 9. (1 point) Problem 7. (1 point) Consider the initial value problem Use the Laplace transform to solve the following initial value y' + 25y = cos(5t), y(0) = 5, y(0) =8. problem: getwollot ob svine o andlaneif casigal out sill (1) Take the Laplace transform of both sides of the given dif- anal dong ferential equation to create the corresponding algebraic y" - 10y + 29y =0 y(0) = 0, y(0) =2 equation. Denote the Laplace transform of y(t) by Y(s). (1) Using Y for the Laplace transform of y(t), i.e., Y = orll a Do not move any terms from one side of the equation to Lly(t) }, find the equation you get by taking the Laplace the other (until you get to part (b) below). ()transform of the differential equation adi to) Y galan ki sdi to help not gaivloe bas nounups followslib (formulas) it avlon wok () (2) Now solve for Y (s = (2) Solve your equation for Y(s). ob noida siting aft al nowam wods adi of W (8) (3) By completing the square in the denominator and invert- Y (s) = [ty(t) } = ing the transform, find dulus adi bal) of solarand coalga y(t) = (3) Take the inverse Laplace transform of both sides of the previous equation to solve for y(t). dwell () y (1) =