The system of first order differential equationsy₁ = −4y₁ +9y2 + 1y₂ = 9y1 - 4y2 + 1y2where y₁ (0) = 0, y₂ (0) = 0has solution19y₁ (t) =y₂ (t) =110 7t 7 -11te63991693e129777t(110e¹t + Te+7e-¹¹¹_117)

We solve it by eigenvalue and eigenvector method.

Answered: The system of first order differential…

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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The system of first order differential equations y₁ = -4y1 +9y2 + 1 Y2 = 9y₁ − 4y2 + 1 where y₁ (0) = 0, y2 (0) = 0 has solution 1 y₁ (t)= y₂(t) = 110 7t 7 -11t e e 99 129 77 (110e7t + 7e¯¹lt – 117) ; ( 9 63 1 693