Let y be a function of t, and suppose Lly]=F(s). Find the transform of the third derivative of y denoted by Lly']. A There is no correct answer among the choices. В s³F(s) – s²y"(0) – sy'(0) – y (0) ©...

Extracted text: Let y be a function of t, and suppose Lly]=F(s). Find the transform of the third derivative of y denoted by Lly']. A There is no correct answer among the choices. В s³F(s) – s²y"(0) – sy'(0) – y (0) © s³F(s) – s²y'(0) – sy"(0) – y'"(0) D s³F(s) – s²y(0) – sy'(0) – y'"(0) E s³F(s)+s?y(0) +sy'(0) +y"(0)


Extracted text: Below are specific steps, labeled by line numbers, in solving by Laplace transforms the initial-value problem y"+3y'+2y =21, y (0) =1, y'(0) = -1 Answer the question about the solution and the specific steps that were shown. Solution: Line 1: L[y"+3y'+2y]=L[2/] Line 2: L[y"]+3Lly']+ 2L[y]=L[2r] Line 3: (s²F(s) – sy (0) – y'(0)) + 3(sF(s) – y(0)) + 2F(s) = Line 4: (s?F(s) – s+ 1) + 3(sF(s) – 1) + 2F(s) = Line 5: (s²+ 3s + 2)F(s) – s-2- Line 6: (s²+ 3s + 2)F(s) = *2 Line 7: F(s) =124N+2) * 3²+ 3s + 2 s+2 2 s+2 Line 8: L-\F(s)]=L-4- 's?(s?+3s+2) * 3²+3s +2 –3/2 1 12 2 Line 9: y = L-'I- S+1 s+2 Line 10: y = 3e - Question: Why is it necessary that the quantities or terms in Line 8 be transformed in the form in Line 9? To generate smaller fractional terms. B) To make more explicit the terms for the inverse transforms. C) There is no correct answer among the choices. To rewrite the terms to obtain an equivalent quantity. E) To get more terms for combining terms. O O O O O