Given the differential equation y" + 4y' - 12y 5x e7* And the Solutions to its Characteristic Equation Characteristic Solutions: R, = -6 and R, = 2 (1) Determine the General Form of the Particular Solution, and (2) Write the General Solution for the Particular Side of the Differential Equation. A y, = [Ax]e7* -6x B 'p = [Ax + B]e + [Cx + D]e2x y, = [Ax]e* cos(x) + [Bx]eT* sin(x) D) y, = [Ax + B]eT* E [Ax? + Bx] e7% Y, = [Ax3 + Bx?] e?x
Given the differential equation y" + 4y' - 12y 5x e7* And the Solutions to its Characteristic Equation Characteristic Solutions: R, = -6 and R, = 2 (1) Determine the General Form of the Particular Solution, and (2) Write the General Solution for the Particular Side of the Differential Equation. A y, = [Ax]e7* -6x B 'p = [Ax + B]e + [Cx + D]e2x y, = [Ax]e* cos(x) + [Bx]eT* sin(x) D) y, = [Ax + B]eT* E [Ax? + Bx] e7% Y, = [Ax3 + Bx?] e?x
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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q11
![Given the differential equation
y" + 4 y' - 12y
5x e 7*
And the Solutions to its Characteristic Equation
Characteristic Solutions: R, = -6 and R, = 2
(1) Determine the General Form of the Particular Solution, and (2) Write the General Solution for the Particular Side of the
Differential Equation.
A yp = [Ax]e7*
-6x
B
'p = [Ax + B]e
+ [Cx + D]e2
y, = [Ax]e* cos(x) + [Bx]e% sin(x)
Dy, [Ax + B]e*
E
y, = [Ax? + Bx]e*
F
Yp = [Ax3 + Bx2] eT*](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F94930702-fbcd-4244-b178-ebe011f78567%2F2a7c9006-154e-4914-bfea-2f99752396fb%2F15ot4q_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Given the differential equation
y" + 4 y' - 12y
5x e 7*
And the Solutions to its Characteristic Equation
Characteristic Solutions: R, = -6 and R, = 2
(1) Determine the General Form of the Particular Solution, and (2) Write the General Solution for the Particular Side of the
Differential Equation.
A yp = [Ax]e7*
-6x
B
'p = [Ax + B]e
+ [Cx + D]e2
y, = [Ax]e* cos(x) + [Bx]e% sin(x)
Dy, [Ax + B]e*
E
y, = [Ax? + Bx]e*
F
Yp = [Ax3 + Bx2] eT*
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