Consider the initial value problem and find the solution: a. y" +5y" + 17y' + 13y = 0, b. y" + 4ay' + (4a² + 1)y = 0, y(0) = -2, y(0) = 2, y'(0) = 2, y'(0) = -3 y"(0) = 0 %3D
Consider the initial value problem and find the solution: a. y" +5y" + 17y' + 13y = 0, b. y" + 4ay' + (4a² + 1)y = 0, y(0) = -2, y(0) = 2, y'(0) = 2, y'(0) = -3 y"(0) = 0 %3D
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
Pls answer letter a. I need the answer asap. Thank you.
![Consider the initial value problem and find the solution:
a. y" + 5y" + 17y' + 13y = 0,
b. y" + 4ay' + (4a² + 1)y = 0,
y(0) = -2,
y(0) = 2,
y'(0) = 2,
y'(0) = -3
y"(0) = 0](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6caf8aef-bacd-41bd-bdc6-4246c28cc197%2Fdd9ac8c3-1f27-40fe-a0cf-a37735acac0f%2Fjyiinao_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Consider the initial value problem and find the solution:
a. y" + 5y" + 17y' + 13y = 0,
b. y" + 4ay' + (4a² + 1)y = 0,
y(0) = -2,
y(0) = 2,
y'(0) = 2,
y'(0) = -3
y"(0) = 0
![Two Distinct Real Roots
y = c1e²1*+ c2edzx
Real Double Root
1 = 11= 12
y = c1e%1*+ c2xedz*
Complex Conjugate Roots
11 = a + ib d2 = a – ib
%3D
y = eax(c1 cos bx + c2 sin bx)
%3D](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6caf8aef-bacd-41bd-bdc6-4246c28cc197%2Fdd9ac8c3-1f27-40fe-a0cf-a37735acac0f%2Ftcje5mh_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Two Distinct Real Roots
y = c1e²1*+ c2edzx
Real Double Root
1 = 11= 12
y = c1e%1*+ c2xedz*
Complex Conjugate Roots
11 = a + ib d2 = a – ib
%3D
y = eax(c1 cos bx + c2 sin bx)
%3D
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