Consider the initial value problem and find the solution: a. y" + 4ay' + (4a² + 1)y = 0, b. 4y" + y' + 5y = 0, y(0) = 2, y(0) = 2, y'(0) = -3 y'(0) = 1, %3D %3D y"(0) = -1 %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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Answer B

y = c1ed1*+ c2e?z*
1 = 11= 12
y = c1ed1*+ c2xe%z*
Two Distinct Real Roots
Real Double Root
Complex Conjugate Roots
1 = a + ib A2 = a – ib
%3D
%3D
y = eax(c1 cos bx + c2 sin bx)
Transcribed Image Text:y = c1ed1*+ c2e?z* 1 = 11= 12 y = c1ed1*+ c2xe%z* Two Distinct Real Roots Real Double Root Complex Conjugate Roots 1 = a + ib A2 = a – ib %3D %3D y = eax(c1 cos bx + c2 sin bx)
Consider the initial value problem and find the solution:
a. y" + 4ay' + (4a² + 1)y = 0,
b. 4y" + y' + 5y = 0,
y(0) = 2,
y(0) = 2,
y'(0) = -3
y'(0) = 1,
y"(0) = -1
%3D
Transcribed Image Text:Consider the initial value problem and find the solution: a. y" + 4ay' + (4a² + 1)y = 0, b. 4y" + y' + 5y = 0, y(0) = 2, y(0) = 2, y'(0) = -3 y'(0) = 1, y"(0) = -1 %3D
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