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1. If L{f(t)} = F(s) then L{f""(t)} is, A) s²F(s)- sf (0) - f'(0) s²F(s)-sf'(0) - f (0) B) s³ F(s) D) s³ F(s) s² f(0) - sf'(0) - f"(0) sf'(0) - f (0)

1. If L{f(t)} = F(s) then L{f""(t)} is, A) s²F(s)- sf (0) - f'(0) s²F(s)-sf'(0) - f (0) B) s³ F(s) D) s³ F(s) s² f(0) - sf'(0) - f"(0) sf'(0) - f (0)

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) A) B) Statement I only Statement II only 2. Which of the following statements is/are true? I. The Laplace transform of y(V) is s4L(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. C A) F(s) = B) F(s) = D) -s +3 1 + (s²2s1) s(s² - 2s-1) 1 s(s²2s1) C) D) s³ F(s) - s² f(0) - sf'(0) - f"(0) s³ F(s) - sf'(0) - f (0) 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 Both statements None of the choices. C) F (s) D) F(s) C) D) = = s+1 (s²2s1) 1 (s²2s-1) 4. Which of the following initial value problem satisfy the given Laplace transform A) y" + y = 0; y(0) = 1; y'(0) = 0 B) y"+y=0; y(0) = 0; y'(0) = 1 + 1 s(s²2s1) L{f(t)} y" + y = 1; y(0) = 0; y'(0) = 0 y" + y = 1; y(0) = 0; y' (0) = 1 1 s² + 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) A) B) Statement I only Statement II only 2. Which of the following statements is/are true? I. The Laplace transform of y(V) is s4L(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. C A) F(s) = B) F(s) = D) -s +3 1 + (s²2s1) s(s² - 2s-1) 1 s(s²2s1) C) D) s³ F(s) - s² f(0) - sf'(0) - f"(0) s³ F(s) - sf'(0) - f (0) 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 Both statements None of the choices. C) F (s) D) F(s) C) D) = = s+1 (s²2s1) 1 (s²2s-1) 4. Which of the following initial value problem satisfy the given Laplace transform A) y" + y = 0; y(0) = 1; y'(0) = 0 B) y"+y=0; y(0) = 0; y'(0) = 1 + 1 s(s²2s1) L{f(t)} y" + y = 1; y(0) = 0; y'(0) = 0 y" + y = 1; y(0) = 0; y' (0) = 1 1 s² + 1 ?
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