1. Please work out the solution for x(t). (1) Find the homogeneous solution: x(t) + 4x(t) + 3x(t) = 0. (Hint: Assume x(t) = = (2) Find the non-homogeneous solution: x(t) + 4x(t) + 3x(t) = 1. (3) Find the non-homogeneous solution: X(t) + 4x(t) + 3x(t) = sin (2t). ceat) 2. Please work out the homogeneous solution for the following 2nd-order ODES. (Hint: Assume x(t) = cet) (1) X(t) + 4x(t) + 4x(t) = 0. (2) X(t) + 4x(t) + 9x(t) = 0.
1. Please work out the solution for x(t). (1) Find the homogeneous solution: x(t) + 4x(t) + 3x(t) = 0. (Hint: Assume x(t) = = (2) Find the non-homogeneous solution: x(t) + 4x(t) + 3x(t) = 1. (3) Find the non-homogeneous solution: X(t) + 4x(t) + 3x(t) = sin (2t). ceat) 2. Please work out the homogeneous solution for the following 2nd-order ODES. (Hint: Assume x(t) = cet) (1) X(t) + 4x(t) + 4x(t) = 0. (2) X(t) + 4x(t) + 9x(t) = 0.
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.CR: Chapter 11 Review
Problem 12CR
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![1. Please work out the solution for x(t).
(1) Find the homogeneous solution: x(t) + 4x(t) + 3x(t) = 0.
(Hint: Assume x(t) = ce^t)
(2) Find the non-homogeneous solution: x(t) + 4x(t) + 3x(t) = 1.
(3) Find the non-homogeneous solution: x(t) + 4x(t) + 3x(t) = sin (2t).
2. Please work out the homogeneous solution for the following 2nd-order ODES.
(Hint: Assume x(t) = cet)
(1) X(t) + 4x(t) + 4x(t) = 0.
(2) X(t) + 4x(t) + 9x(t) = 0.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F995b01c6-0baf-4a59-9e51-957b551c07e4%2Ffbfdbe8f-45f0-44a1-ba86-90dbcbcea874%2F3ssfoh_processed.png&w=3840&q=75)
Transcribed Image Text:1. Please work out the solution for x(t).
(1) Find the homogeneous solution: x(t) + 4x(t) + 3x(t) = 0.
(Hint: Assume x(t) = ce^t)
(2) Find the non-homogeneous solution: x(t) + 4x(t) + 3x(t) = 1.
(3) Find the non-homogeneous solution: x(t) + 4x(t) + 3x(t) = sin (2t).
2. Please work out the homogeneous solution for the following 2nd-order ODES.
(Hint: Assume x(t) = cet)
(1) X(t) + 4x(t) + 4x(t) = 0.
(2) X(t) + 4x(t) + 9x(t) = 0.
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