Suppose a system of differential equations yields eigenvalue λ=1+3i with2+ieigenvector =Find any real-valued solution.

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Answered: Suppose a system of 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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Question

Suppose a system of differential equations yields eigenvalue λ=1+3i with
2+i
eigenvector =
Find any real-valued solution.

Expert Solution

Step 1: Determine the given variables

$Given space that The space eigen space value space space straight lambda subscript 1 equals 1 plus 3 i space This space is space in space the space form space lambda subscript 1 equals alpha plus beta i Here space space alpha equals 1 space space comma space space beta equals 3 The space eigenvector space omega with rightwards arrow on top equals open square brackets table row cell 2 plus i end cell row 1 end table close square brackets equals open square brackets table row 2 row 1 end table close square brackets plus straight i open square brackets table row 1 row 0 end table close square brackets This space is space in space the space form space omega with rightwards arrow on top equals u subscript 1 plus i u subscript 2 Here space space u subscript 1 equals open square brackets table row 2 row 1 end table close square brackets space space comma space space u subscript 2 equals open square brackets table row 1 row 0 end table close square brackets$