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7.5. y' + 4y + 5y = 0, y(0) = 1, y'(0) = 0

7.5. y' + 4y + 5y = 0, y(0) = 1, y'(0) = 0

Advanced Engineering Mathematics
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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solve 7.5

7 Second Order Equations with Complex Roots See also: Section 3.3 in Boyce and DiPrima or 2.2.1 in Braun. Solve the following differential equations: 7.1. y" - 2y + 2y = 0 7.2. 4y" +9y=0 7.3. y' + 6y + 13y = 0 7.4. 9y" + 6y + 4y = 0 7.5. y' + 4y + 5y = 0, y(0) = 1, y'(0) = 0 7.6. y"+y+1.25y = 0, y(0) = 3, y'(0) = 1
Transcribed Image Text:7 Second Order Equations with Complex Roots See also: Section 3.3 in Boyce and DiPrima or 2.2.1 in Braun. Solve the following differential equations: 7.1. y" - 2y + 2y = 0 7.2. 4y" +9y=0 7.3. y' + 6y + 13y = 0 7.4. 9y" + 6y + 4y = 0 7.5. y' + 4y + 5y = 0, y(0) = 1, y'(0) = 0 7.6. y"+y+1.25y = 0, y(0) = 3, y'(0) = 1
Expert Solution
Step 1: Given:

y apostrophe apostrophe plus 4 y apostrophe plus 5 y equals 0 semicolon space space space space space space space y open parentheses 0 close parentheses equals 1 comma space y apostrophe open parentheses 0 close parentheses equals 0

We have to solve the given differential equation.

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