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1. 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) s°F(s) – s²f(0) – sf'(0) – f"(0) D) s°F(s) – sf'(0) – f(0) 2. Which of the following statements is/are true? 1. The Laplace transform of y) 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 3. 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 s+1 1 A) F(s) = (s² – 2s - 1) s(s² – 2s – 1) C) F(s) = (s² – 2s – 1) s(s² – 2s – 1) 1 B) F(s) = D) F(s) = s(s² – 2s – 1) (s² – 2s – 1) 4. Which of the following initial value problem satisfy the given Laplace transform L{f(t)} 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

1. 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) s°F(s) – s²f(0) – sf'(0) – f"(0) D) s°F(s) – sf'(0) – f(0) 2. Which of the following statements is/are true? 1. The Laplace transform of y) 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 3. 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 s+1 1 A) F(s) = (s² – 2s - 1) s(s² – 2s – 1) C) F(s) = (s² – 2s – 1) s(s² – 2s – 1) 1 B) F(s) = D) F(s) = s(s² – 2s – 1) (s² – 2s – 1) 4. Which of the following initial value problem satisfy the given Laplace transform L{f(t)} 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

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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1. 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) 2. Which of the following statements is/are true? 1. The Laplace transform of y(V) 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 3. 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 1 A) F(s) = C) F(s) = (s² – 2s – 1) * s(s² – 2s – 1) (s² – 2s – 1) * s(s² – 2s – 1) 1 1. B) F(s) = D) F(s) = s(s² – 2s – 1) - 2s – 1) 1 4. 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
Transcribed Image Text:1. 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) 2. Which of the following statements is/are true? 1. The Laplace transform of y(V) 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 3. 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 1 A) F(s) = C) F(s) = (s² – 2s – 1) * s(s² – 2s – 1) (s² – 2s – 1) * s(s² – 2s – 1) 1 1. B) F(s) = D) F(s) = s(s² – 2s – 1) - 2s – 1) 1 4. 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
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