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6 Determine whether any of the functions (a) y₁ = sin 2x, (b) y₂(x) = x, or (c) y3 (x) = sin 2x is a solution to the initial-value problem y" + 4y = 0; y(0) = 0, y (0) = 1.

6 Determine whether any of the functions (a) y₁ = sin 2x, (b) y₂(x) = x, or (c) y3 (x) = sin 2x is a solution to the initial-value problem y" + 4y = 0; y(0) = 0, y (0) = 1.

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter11: Differential Equations
Section11.1: Solutions Of Elementary And Separable Differential Equations
Problem 5E
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1 Find the explicit solution to the equation L dI + RI dt 0 2 Determine the order, unknown function, and the independent variable in each of the following differential equations: 10 3 (a) (c) 8 - 5xy' = et + 1 d't ds2 (a) dt + st = s ds d²x = y = y² + 1 dy² (c) 2x + 3x - 5x = 0 (b) (d) tÿ+t²y−(sint)√√y=t² −1 (b) (a) y=x₂ 5 Determine the order, unknown function, and the independent variable in each of the following differential equations: 5 Is y(x) = 1 a solution of y" + 2y' + y = x? y (b) y=x8x², + 7 dx dy (d) 17y(4) — 16(2) - 4.2y³ = 3 cos t db dp 4 Determine whether y(x) = 2e¯* + xe¯ is a solution of y" + 2y' + y = 0. 10 x² +1 6 Determine whether any of the functions (a) y₁ = sin 2x, (b) y₂(x) = x, or (c) y²3 (x) = sin 2x is a solution to the initial-value problem y" + 4y = 0; y(0) = 0, y (0) = 1. (c) −1+1 7 Which of the following functions are solutions of the differential equation y' – 5y = 0? (a) y = 5, (b) y = 5x, (c) y=x³, (d) y=e³x, (e) y=2e5x, (f) y = 5e²x Which of the following functions are solutions of the differential equation y' – 3y = 6? (a) y=-2, (b) y = 0, (c) y=e³x-2, (d) y=e²x-3, (e) y = 4e³x - 2 + b² − b² = p 9 Which of the following functions are solutions of the differential equation dy 2y + x² dx xy y = = √√x³ − x¹, (d) y = (x8x4) ¹/4 Which of the following functions are solutions of the differential equation x − 4x + 4x = e (a) x=e¹, (b) x=e²t (c) x = e²t + e¹, (d) x=te²t + e¹, (e) x = e²t + tet
Transcribed Image Text:1 Find the explicit solution to the equation L dI + RI dt 0 2 Determine the order, unknown function, and the independent variable in each of the following differential equations: 10 3 (a) (c) 8 - 5xy' = et + 1 d't ds2 (a) dt + st = s ds d²x = y = y² + 1 dy² (c) 2x + 3x - 5x = 0 (b) (d) tÿ+t²y−(sint)√√y=t² −1 (b) (a) y=x₂ 5 Determine the order, unknown function, and the independent variable in each of the following differential equations: 5 Is y(x) = 1 a solution of y" + 2y' + y = x? y (b) y=x8x², + 7 dx dy (d) 17y(4) — 16(2) - 4.2y³ = 3 cos t db dp 4 Determine whether y(x) = 2e¯* + xe¯ is a solution of y" + 2y' + y = 0. 10 x² +1 6 Determine whether any of the functions (a) y₁ = sin 2x, (b) y₂(x) = x, or (c) y²3 (x) = sin 2x is a solution to the initial-value problem y" + 4y = 0; y(0) = 0, y (0) = 1. (c) −1+1 7 Which of the following functions are solutions of the differential equation y' – 5y = 0? (a) y = 5, (b) y = 5x, (c) y=x³, (d) y=e³x, (e) y=2e5x, (f) y = 5e²x Which of the following functions are solutions of the differential equation y' – 3y = 6? (a) y=-2, (b) y = 0, (c) y=e³x-2, (d) y=e²x-3, (e) y = 4e³x - 2 + b² − b² = p 9 Which of the following functions are solutions of the differential equation dy 2y + x² dx xy y = = √√x³ − x¹, (d) y = (x8x4) ¹/4 Which of the following functions are solutions of the differential equation x − 4x + 4x = e (a) x=e¹, (b) x=e²t (c) x = e²t + e¹, (d) x=te²t + e¹, (e) x = e²t + tet
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