Developmental Mathematics (9th Edition)
9th Edition
ISBN: 9780321997173
Author: Marvin L. Bittinger, Judith A. Beecher
Publisher: PEARSON
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Chapter H, Problem 14ES
To determine
To calculate: The solution of the equation
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Solve Problem I, 4, from the Shushu jiuzhang, which
is equivalent to N = 0 (mod 11), N = 0 (mod 5), N = 4
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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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What is the solution of the initial value problem?
4) Consider the initial value problem
"
8y +30y+25y = 0, y(0) = -2, y (0) = 8
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Chapter H Solutions
Developmental Mathematics (9th Edition)
Ch. H - Solve: | x |=6. Then graph on the number line.Ch. H - Prob. 2DECh. H - Prob. 3DECh. H - Prob. 4DECh. H - Prob. 5DECh. H - Prob. 6DECh. H - Prob. 7DECh. H - Prob. 8DECh. H - Prob. 9DECh. H - Prob. 1ES
Ch. H - Prob. 2ESCh. H - Prob. 3ESCh. H - Prob. 4ESCh. H - Prob. 5ESCh. H - Prob. 6ESCh. H - Prob. 7ESCh. H - Prob. 8ESCh. H - Prob. 9ESCh. H - Prob. 10ESCh. H - Prob. 11ESCh. H - Prob. 12ESCh. H - Prob. 13ESCh. H - Prob. 14ESCh. H - Prob. 15ESCh. H - Prob. 16ESCh. H - Prob. 17ESCh. H - Prob. 18ESCh. H - Prob. 19ESCh. H - Prob. 20ESCh. H - Prob. 21ESCh. H - Prob. 22ESCh. H - Prob. 23ESCh. H - Prob. 24ESCh. H - Prob. 25ESCh. H - Prob. 26ESCh. H - Prob. 27ESCh. H - Prob. 28ESCh. H - Prob. 29ESCh. H - Prob. 30ESCh. H - Prob. 31ESCh. H - Prob. 32ESCh. H - Prob. 33ESCh. H - Prob. 34ESCh. H - Prob. 35ESCh. H - Prob. 36ES
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- 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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