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x₁ = 9x₁ +5x2, x₂ = -6x₁-2x2; x₁ (0)=1, x₂ (0) = 0 /

x₁ = 9x₁ +5x2, x₂ = -6x₁-2x2; x₁ (0)=1, x₂ (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 6 and 9 please
5.2 Problems In Problems 1 through 16, apply the eigenvalue method of this section to find a general solution of the given system. If initial values are given, find also the corresponding particular solution. 1. x₁ = x₁ + 2x2, x₂ = 2x₁ + x₂ 2. x₁ = 2x₁ + 3x2, x₂ = 2x₁ + x2 3. x = 3x₁ + 4x2, 4. x₁ = 4x₁ + x₂, x₂ = 6x₁ - x₂ 5. x = 6x₁7x2, x₂ = x₁ - 2x₂ 6. x₁ = 9x₁ +5x2, x₂ = -6x₁-2x2; x₁ (0) = 1, x₂ (0) = 0 7. x = -3x₁ +4x2, x₂ = 6x₁ - 5x₂ 8. x = x − 5X2, X = x - 2 9. x₁ = 2x₁ - 5x2, 10. x = -3x₁2x2, x₂ = 9x₁ + 3x₂ x₂ = 3x₁ + 2x2; x₁ (0) = x₂(0) = 1 x₂ = 4x1 - 2x2; x₁ (0) = 2, x₂ (0) = 3 11. x = x₁ - 2x₂, x₂ = 2x₁ + x₂; x₁ (0) = 0, x₂ (0) = 4 12. x = x₁ - 5x2, x₂ = x₁ + 3x₂ x₂ = 2x1 - x2 13. x = 5x₁9x2, 14. x = 3x₁ - 4x2, x₂ = 4x₁ + 3x2 15. x₁ = 7x₁5x2, x₂ = 4x₁ + 3x₂ 16. x = -50x₁ + 20x2, x2 = 100x₁60x2
Transcribed Image Text:5.2 Problems In Problems 1 through 16, apply the eigenvalue method of this section to find a general solution of the given system. If initial values are given, find also the corresponding particular solution. 1. x₁ = x₁ + 2x2, x₂ = 2x₁ + x₂ 2. x₁ = 2x₁ + 3x2, x₂ = 2x₁ + x2 3. x = 3x₁ + 4x2, 4. x₁ = 4x₁ + x₂, x₂ = 6x₁ - x₂ 5. x = 6x₁7x2, x₂ = x₁ - 2x₂ 6. x₁ = 9x₁ +5x2, x₂ = -6x₁-2x2; x₁ (0) = 1, x₂ (0) = 0 7. x = -3x₁ +4x2, x₂ = 6x₁ - 5x₂ 8. x = x − 5X2, X = x - 2 9. x₁ = 2x₁ - 5x2, 10. x = -3x₁2x2, x₂ = 9x₁ + 3x₂ x₂ = 3x₁ + 2x2; x₁ (0) = x₂(0) = 1 x₂ = 4x1 - 2x2; x₁ (0) = 2, x₂ (0) = 3 11. x = x₁ - 2x₂, x₂ = 2x₁ + x₂; x₁ (0) = 0, x₂ (0) = 4 12. x = x₁ - 5x2, x₂ = x₁ + 3x₂ x₂ = 2x1 - x2 13. x = 5x₁9x2, 14. x = 3x₁ - 4x2, x₂ = 4x₁ + 3x2 15. x₁ = 7x₁5x2, x₂ = 4x₁ + 3x₂ 16. x = -50x₁ + 20x2, x2 = 100x₁60x2
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