For Part I, answer letters a-e: a. If L{f(t)} = F(s) then L{f''(t)} is, A) s²F(s) – sf(0) – f'(0) B) s²F(s) – sf'(0) – f(0) C) s³F(s) – s²f(0) – sf'(0) – f"(0) D) s³F(s) – sf'(0) – f(0) b. Which of the following statements is/are true? I. The Laplace transform of y(V) is sʻL(y) - s³y(0) – s²y'(0) – sy"(0) – y'"(0). II. When solved using Laplace transforms, a higher order linear ODE with constant coefficients with available initial conditions yields a general solution. A) Statement 1 only B) Statement 2 only C) Both statements D) None of the choices c. What is the Laplace transform of the differential equation and initial value conditions given below? у" - 2у'— у %3D 13 y(0) = -1; y'(0) = 1 -s+3 s+1 A) F(s) =' C) F(s) = (s²–2s–1) s(s²-2s-1) (s²–2s–1) s(s²-25-1) D) F(s) = -25-1) 1 B) F(s) = s(s²-2s-1) d. Which of the following initial value problem satisfy the given Laplace transform? L{f(t)} : s² + 1 A) y" + y = 0; y(0) = 1;y'(0) = 0 B) y" + y = 0; y(0) = 0; y'(0) = 1 C) y" + y = 1; y(0) = 0; y'(0) = 0 D) y" + y = 1; y(0) = 0; y'(0) = 1
For Part I, answer letters a-e: a. If L{f(t)} = F(s) then L{f''(t)} is, A) s²F(s) – sf(0) – f'(0) B) s²F(s) – sf'(0) – f(0) C) s³F(s) – s²f(0) – sf'(0) – f"(0) D) s³F(s) – sf'(0) – f(0) b. Which of the following statements is/are true? I. The Laplace transform of y(V) is sʻL(y) - s³y(0) – s²y'(0) – sy"(0) – y'"(0). II. When solved using Laplace transforms, a higher order linear ODE with constant coefficients with available initial conditions yields a general solution. A) Statement 1 only B) Statement 2 only C) Both statements D) None of the choices c. What is the Laplace transform of the differential equation and initial value conditions given below? у" - 2у'— у %3D 13 y(0) = -1; y'(0) = 1 -s+3 s+1 A) F(s) =' C) F(s) = (s²–2s–1) s(s²-2s-1) (s²–2s–1) s(s²-25-1) D) F(s) = -25-1) 1 B) F(s) = s(s²-2s-1) d. Which of the following initial value problem satisfy the given Laplace transform? L{f(t)} : s² + 1 A) y" + y = 0; y(0) = 1;y'(0) = 0 B) y" + y = 0; y(0) = 0; y'(0) = 1 C) y" + y = 1; y(0) = 0; y'(0) = 0 D) y" + y = 1; y(0) = 0; y'(0) = 1
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Please answer this NEATLY, COMPLETELY, and CORRECTLY for an UPVOTE.
Transcribed Image Text:For Part I, answer letters a-e:
a. If L{f(t)} = F(s) then L{f'''(t)} is,
A) s²F(s) – sf(0) – f'(0)
B) s²F(s) – sf'(0)– f(0)
C) s³F(s) – s²f(0) – sf'(0) – f"(0)
D) s°F(s) – sf'(0) – f(0)
b. Which of the following statements is/are true?
I. The Laplace transform of y(W) is s*L(y) – s³y(0) – s²y'(0) – sy"(0) – y"'(0).
II. When solved using Laplace transforms, a higher order linear ODE with constant
coefficients with available initial conditions yields a general solution.
A) Statement 1 only
B) Statement 2 only
C) Both statements
D) None of the choices
c. What is the Laplace transform of the differential equation and initial value conditions given
below?
y" – 2y' – y = 1;
y(0) = -1;
y'(0) = 1
-s+3
1
s+1
A) F(s) =
s(s2-25-1)
C) F(s) =
(s2-25-1)
(s2-25-1)
s(s2-2s-1)
1
B) F(s) =
s(s2-2s-1)
D) F(s) =
(s2-2s-1)
d. Which of the following initial value problem satisfy the given Laplace transform?
1
L{f(t)}
s2 + 1
A) y" + y = 0; y(0) = 1; y'(0) = 0
B) y" + y = 0; y(0) = 0; y'(0) = 1
C) y" + y = 1; y(0) = 0; y'(0) = 0
D) y" + y = 1; y(0) = 0; y'(0) = 1
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