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a) Which of the following is an initial value problem (IVP) of 2nd-order linear ODE OI OII O III, where I:y" —25 y, y(0) = 1, y′(0) = −1 II:y” = −25 y, y(0) = 1, y'(2) = 0, III:y" = -25 y², y(0) = 1, y' (2) = 0. = b) The initial conditions in the above IVP in a) refers to the xỏ value 0x0 = 2 xo 0 Oxo = 0 or xo = 2. = c) The solution(s) of the I.V.P. in a) is/are O II and III OII OI where I:y(x) = cos (5x) – ½ sin (5x), II:y(x) = A cos (5x) + B sin (5x), where A and B are arbitrary real constants, III:y(x) = C₁e5ix + C₂e-5ix, where C₁ and C₂ are arbitrary complex constants.

a) Which of the following is an initial value problem (IVP) of 2nd-order linear ODE OI OII O III, where I:y" —25 y, y(0) = 1, y′(0) = −1 II:y” = −25 y, y(0) = 1, y'(2) = 0, III:y" = -25 y², y(0) = 1, y' (2) = 0. = b) The initial conditions in the above IVP in a) refers to the xỏ value 0x0 = 2 xo 0 Oxo = 0 or xo = 2. = c) The solution(s) of the I.V.P. in a) is/are O II and III OII OI where I:y(x) = cos (5x) – ½ sin (5x), II:y(x) = A cos (5x) + B sin (5x), where A and B are arbitrary real constants, III:y(x) = C₁e5ix + C₂e-5ix, where C₁ and C₂ are arbitrary complex constants.

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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a) Which of the following is an initial value problem (IVP) of 2nd-order linear ODE OI OII O III, where I:y" = −25 y, y(0) = 1, y' (0) = −1 II:y" = -25 y, y(0) = 1, y' (2) = 0, III:y" = -25y², y(0) = 1, y' (2) = 0. b) The initial conditions in the above IVP in a) refers to the xo value 2. 2 Ο ×0 хо - 0 Ο χο XO c) The solution(s) of the I.V.P. in a) is/are O II and IIIOII OI where I:y(x) = cos (5x) – sin (5x), ½-¹ - = 0 or xo = II: y(x) = A cos (5x) + B sin (5x), where A and B are arbitrary real constants, III:y(x) = C₁e5ix + C₂e-5ix, where C₁ and C₂ are arbitrary complex constants.
Transcribed Image Text:a) Which of the following is an initial value problem (IVP) of 2nd-order linear ODE OI OII O III, where I:y" = −25 y, y(0) = 1, y' (0) = −1 II:y" = -25 y, y(0) = 1, y' (2) = 0, III:y" = -25y², y(0) = 1, y' (2) = 0. b) The initial conditions in the above IVP in a) refers to the xo value 2. 2 Ο ×0 хо - 0 Ο χο XO c) The solution(s) of the I.V.P. in a) is/are O II and IIIOII OI where I:y(x) = cos (5x) – sin (5x), ½-¹ - = 0 or xo = II: y(x) = A cos (5x) + B sin (5x), where A and B are arbitrary real constants, III:y(x) = C₁e5ix + C₂e-5ix, where C₁ and C₂ are arbitrary complex constants.
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