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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) C) D) s³F(s)-s²f (0) - sf'(0) - f"(0) S³F (s)- 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) C) D) s³F(s)-s²f (0) - sf'(0) - f"(0) S³F (s)- sf'(0)-f(0)

Calculus: Early Transcendentals
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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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) 2. Which of the following statements is/are true? I. The Laplace transform of y() 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. A) B) Statement 1 only Statement 2 only A) F(s) = B) F(s): C) s³F(s)-s²f (0) - sf'(0) - f" (0) D) s³F(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 -s +3 1 + (s²2s1) s(s² - 2s - 1) 1 s(s² - 2s - 1) C) D) Both statements None of the choices C) F(s) = D) F(s) = C) D) s+1 1 + (s²2s1) s(s² - 2s-1) 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 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) 2. Which of the following statements is/are true? I. The Laplace transform of y() 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. A) B) Statement 1 only Statement 2 only A) F(s) = B) F(s): C) s³F(s)-s²f (0) - sf'(0) - f" (0) D) s³F(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 -s +3 1 + (s²2s1) s(s² - 2s - 1) 1 s(s² - 2s - 1) C) D) Both statements None of the choices C) F(s) = D) F(s) = C) D) s+1 1 + (s²2s1) s(s² - 2s-1) 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 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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