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
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Chapter1: Functions And Models
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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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