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Given the differential equation y"- 8y' +16y=- 3e**. a) Find the complementary solution y. to the differential equation. b) Write down the FORM of the particular solution yp for a solution using undetermined coefficients. DO NOT solve for Yp. Use Table 4.4.1 Yp =

Given the differential equation y"- 8y' +16y=- 3e**. a) Find the complementary solution y. to the differential equation. b) Write down the FORM of the particular solution yp for a solution using undetermined coefficients. DO NOT solve for Yp. Use Table 4.4.1 Yp =

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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Given the differential equation y"- 8y' +16y=- 3e**. 4. a) Find the complementary solution Y. to the differential equation. b) Write down the FORM of the particular solution yp for a solution using undetermined coefficients. DO NOT solve for yp. Use Table 4.4.1 Yp =
Transcribed Image Text:Given the differential equation y"- 8y' +16y=- 3e**. 4. a) Find the complementary solution Y. to the differential equation. b) Write down the FORM of the particular solution yp for a solution using undetermined coefficients. DO NOT solve for yp. Use Table 4.4.1 Yp =
Section 4.4_Undetermined Coefficients TABLE 4.4.1 Trial Particular Solutions g(x) Form of y, 1. 1 (any constant) A 2. 5x + 7 3. Зх? — 2 4. x³ – x + 1 5. sin 4x 6. cos 4.x 7. e$x 8. (9x – 2)e5* 9. x²e$x 10. e3x sin 4x 11. 5x? sin 4x 12. xe3* cos 4x Ах + B Ax² + Bx + C Ax³ + Bx? + Cx + E A cos 4x + B sin 4x A cos 4x + B sin 4x Ae³x (Ax + B)e$x (Ax² + Bx + C)eSx Ae3* cos 4x + Be* sin 4x (Ax² + Bx + C) cos 4x + (Ex² + Fx + G) sin 4x (Ax + B)e3* cos 4x + (Cx + E)e3* sin 4x
Transcribed Image Text:Section 4.4_Undetermined Coefficients TABLE 4.4.1 Trial Particular Solutions g(x) Form of y, 1. 1 (any constant) A 2. 5x + 7 3. Зх? — 2 4. x³ – x + 1 5. sin 4x 6. cos 4.x 7. e$x 8. (9x – 2)e5* 9. x²e$x 10. e3x sin 4x 11. 5x? sin 4x 12. xe3* cos 4x Ах + B Ax² + Bx + C Ax³ + Bx? + Cx + E A cos 4x + B sin 4x A cos 4x + B sin 4x Ae³x (Ax + B)e$x (Ax² + Bx + C)eSx Ae3* cos 4x + Be* sin 4x (Ax² + Bx + C) cos 4x + (Ex² + Fx + G) sin 4x (Ax + B)e3* cos 4x + (Cx + E)e3* sin 4x
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