Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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Solve Problem I, 4, from the Shushu jiuzhang, which
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19) Consider this initial value problem:
y' + y = 2y = -21² + 2t+ 14, y(0) = 0, y (0) = 0
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Chapter 15 Solutions
Advanced Engineering Mathematics
Ch. 15.1 - Prob. 1PCh. 15.1 - Prob. 2PCh. 15.1 - Prob. 3PCh. 15.1 - Prob. 4PCh. 15.1 - Prob. 5PCh. 15.1 - Prob. 6PCh. 15.1 - Prob. 7PCh. 15.1 - Prob. 8PCh. 15.1 - Prob. 9PCh. 15.1 - Prob. 10P
Ch. 15.1 - Prob. 12PCh. 15.1 - Prob. 13PCh. 15.1 - Prob. 14PCh. 15.1 - Prob. 15PCh. 15.1 - Prob. 16PCh. 15.1 - Prob. 17PCh. 15.1 - Prob. 18PCh. 15.1 - Prob. 19PCh. 15.1 - Prob. 20PCh. 15.1 - Prob. 21PCh. 15.1 - Prob. 22PCh. 15.1 - Prob. 23PCh. 15.1 - Prob. 24PCh. 15.1 - Prob. 25PCh. 15.1 - Prob. 26PCh. 15.1 - Prob. 27PCh. 15.1 - Prob. 29PCh. 15.1 - Prob. 30PCh. 15.2 - Prob. 1PCh. 15.2 - Prob. 2PCh. 15.2 - Prob. 3PCh. 15.2 - Prob. 4PCh. 15.2 - Prob. 5PCh. 15.2 - Prob. 6PCh. 15.2 - Prob. 7PCh. 15.2 - Prob. 8PCh. 15.2 - Prob. 9PCh. 15.2 - Prob. 10PCh. 15.2 - Prob. 11PCh. 15.2 - Prob. 12PCh. 15.2 - Prob. 13PCh. 15.2 - Prob. 14PCh. 15.2 - Prob. 15PCh. 15.2 - Prob. 16PCh. 15.2 - Prob. 17PCh. 15.2 - Prob. 18PCh. 15.3 - Prob. 1PCh. 15.3 - Prob. 2PCh. 15.3 - Prob. 3PCh. 15.3 - Prob. 4PCh. 15.3 - Prob. 5PCh. 15.3 - Prob. 6PCh. 15.3 - Prob. 7PCh. 15.3 - Prob. 8PCh. 15.3 - Prob. 9PCh. 15.3 - Prob. 10PCh. 15.3 - Prob. 11PCh. 15.3 - Prob. 12PCh. 15.3 - Prob. 13PCh. 15.3 - Prob. 14PCh. 15.3 - Prob. 15PCh. 15.3 - Prob. 16PCh. 15.3 - Prob. 17PCh. 15.3 - Prob. 18PCh. 15.3 - Prob. 19PCh. 15.4 - Prob. 1PCh. 15.4 - Prob. 2PCh. 15.4 - Prob. 3PCh. 15.4 - Prob. 4PCh. 15.4 - Prob. 5PCh. 15.4 - Prob. 6PCh. 15.4 - Prob. 7PCh. 15.4 - Prob. 8PCh. 15.4 - Prob. 9PCh. 15.4 - Prob. 10PCh. 15.4 - Prob. 11PCh. 15.4 - Prob. 12PCh. 15.4 - Prob. 13PCh. 15.4 - Prob. 14PCh. 15.4 - Prob. 16PCh. 15.4 - Prob. 18PCh. 15.4 - Prob. 19PCh. 15.4 - Prob. 20PCh. 15.4 - Prob. 21PCh. 15.4 - Prob. 22PCh. 15.4 - Prob. 23PCh. 15.4 - Prob. 24PCh. 15.4 - Prob. 25PCh. 15.5 - Prob. 2PCh. 15.5 - Prob. 3PCh. 15.5 - Prob. 4PCh. 15.5 - Prob. 5PCh. 15.5 - Prob. 6PCh. 15.5 - Prob. 7PCh. 15.5 - Prob. 8PCh. 15.5 - Prob. 9PCh. 15.5 - Prob. 10PCh. 15.5 - Prob. 11PCh. 15.5 - Prob. 12PCh. 15.5 - Prob. 13PCh. 15.5 - Prob. 14PCh. 15.5 - Prob. 15PCh. 15.5 - Prob. 16PCh. 15.5 - Prob. 17PCh. 15 - Prob. 1RQCh. 15 - Prob. 2RQCh. 15 - Prob. 3RQCh. 15 - Prob. 4RQCh. 15 - Prob. 5RQCh. 15 - Prob. 6RQCh. 15 - Prob. 7RQCh. 15 - Prob. 8RQCh. 15 - Prob. 9RQCh. 15 - Prob. 10RQCh. 15 - Prob. 11RQCh. 15 - Prob. 12RQCh. 15 - Prob. 13RQCh. 15 - Prob. 14RQCh. 15 - Prob. 15RQCh. 15 - Prob. 16RQCh. 15 - Prob. 17RQCh. 15 - Prob. 18RQCh. 15 - Prob. 19RQCh. 15 - Prob. 20RQCh. 15 - Prob. 21RQCh. 15 - Prob. 22RQCh. 15 - Prob. 23RQCh. 15 - Prob. 24RQCh. 15 - Prob. 25RQCh. 15 - Prob. 26RQCh. 15 - Prob. 27RQCh. 15 - Prob. 28RQCh. 15 - Prob. 29RQCh. 15 - Prob. 30RQ
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- 4) Consider the initial value problem " 8y +30y+25y = 0, y(0) = -2, y (0) = 8 What is the t-coordinate of the local extreme value of y = y(t) on the interval (0, ∞)? Enter your answer as a decimal accurate to three decimal places.arrow_forward10) Which of the following is the general solution of the homogeneous second-order differential equation y + 8y + 52y=0? Here, C, C₁, and C2 are arbitrary real constants. A) y = C₁ecos(61) + C₂e*sin(61) + C B) y = et (sin(4t) + cos(6t)) + C C) y = C₁esin(6) + C₂e+ cos(6t) + C D) y = C₁esin(6) + C₂e+cos(6) E) y=e(C₁sin(61) + C₂cos(61))arrow_forward3) Consider the initial value problem ' y' + 8y = 0, y(0) = -4, y (0) = 16 What is the solution of this initial value problem? A) y = -4t - 2e8t D) y = -4 + 2e-8t B) y = -2 + 2e8t C) y = -2 -2e-8t E) y = -4+ 2e8t F) y = -2t-2e-8tarrow_forward
- 6) Consider the initial value problem y + cos πι + e²бty = 0, y(-1) = 0, y' (-1) = 0 Which of these statements are true? Select all that apply. A) There exists a nonzero real number r such that y(t) = ert is a solution of the initial value problem. B) The constant function y(t) = -1 is a solution of this initial value problem for all real numbers t. C) The constant function y(t) = 0 is the unique solution of this initial value problem on the interval (-∞, ∞). D) This initial value problem has only one solution on the interval (-7, 5). E) There must exist a function y = q(t) that satisfies this initial value problem on the interval (-7,∞).arrow_forward7) Compute the Wronskian of the pair of functions sin(5t) and cos(5t). A) -5 B) 4 C) 1 D) -4 E) 5arrow_forward8) The pair of functions y₁ = eбt and y₁ = teбt forms a fundamental set of solutions for the differential equation y'' - 12y' + 36y= 0.arrow_forward
- 6) Consider the initial value problem y + cos πι + e²бty = 0, y(-1) = 0, y' (-1) = 0 Which of these statements are true? Select all that apply. A) There exists a nonzero real number r such that y(t) = ert is a solution of the initial value problem. B) The constant function y(t) = -1 is a solution of this initial value problem for all real numbers t. C) The constant function y(t) = 0 is the unique solution of this initial value problem on the interval (-∞, ∞). D) This initial value problem has only one solution on the interval (-7, 5). E) There must exist a function y = q(t) that satisfies this initial value problem on the interval (-7,∞).arrow_forward5) Consider the initial value problem 9 (8² 9t+ 1)y' - 8ty = sin(2πt), ) = -4, y = -3.5 16 16 On which of these intervals is this initial value problem certain to have a unique twice differentiable solution? Select all that apply. A) (-∞, ∞) B) (0, 1) 25 C) (-4, -3.5) D) E) 32'32 明arrow_forward1) Which of the following are solutions to the homogeneous second-order differential equation 4y 7y -2y=0? Select all that apply. A) YA = Ce2t, where C is any real constant B) y = 2e-21 6 2t C) y = C (e- 21 + e21), where C is any real constant D) 1/3 = 8 (221 + €21) E) y2 = Ce 2t, where C is any real constant 2t F) y₁ = 8e +2e2t G) y5 = (C₁ e²) · (C₂e-21), where C₁ and C₂ are any real constants 1arrow_forward
- 7) Compute the Wronskian of the pair of functions sin(5t) and cos(5t). A) -5 B) 4 C) 1 D) -4 E) 5arrow_forward5) Consider the initial value problem 9 (8² 9t+ 1)y' - 8ty = sin(2πt), ) = -4, y = -3.5 16 16 On which of these intervals is this initial value problem certain to have a unique twice differentiable solution? Select all that apply. A) (-∞, ∞) B) (0, 1) 25 C) (-4, -3.5) D) E) 32'32 明arrow_forward2) For which of these differential equations is the characteristic equation given by r(10r + 1) = 0? A) y (10y + 1) = 0 B) 10y'' + 1 = 0 C) 10y+1y=0 D) y (10y + 1y) = 0 E) 10y'' + 1y=0arrow_forward
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