1. Consider the ODE systemy' (t) = - (²₂2) Y.y.(a) Why doesn't our usual method (find the eigenvalue-eigenvector pairs and build thegeneral solution y(t) = c₁etvt + c₂ed2tv2) work in this case?(b) Find the general solution of the system by back-substitution: solve the second equa-tion for y2 (t) first, then plug y2 (t) into the y₁ equation to get a solvable scalar ODE.This method only works for systems where the matrix is triangular.

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Answered: 1. Consider the ODE system y' (t) = -…

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 the following differential system: ¤(0) y(0) 2 with 3 Hint. One eigenvalue and its corresponding eigenvector of A are r = -2+i, uį = r(t) 24 cost ae Then you obtain -2e 4(cost + sin t) Please type in a :
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