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Unformatted text preview: on ohms , , the system of differential equations is farads and henrys , the eigenvalue problem is
. . The characteristic equation of the system is Setting
that , the algebraic equations reduce to
Hence one complexvalued solution is , with eigenvalues . It follows ________________________________________________________________________
page 398 —————————————————————————— CHAPTER 7. —— Therefore the general solution is . Imposing the initial conditions, we arrive at the equations
and and , . Since the eigenvalues have negative real parts, all solutions converge to the origin.
26 . The characteristic equation of the system is
, with eigenvalues The eigenvalues are real and different provided that
.
The eigenvalues are complex conjugates as long as . With the specified values, the eigenvalues are
corresponding to
is
is The eigenvector
Hence one complexvalued solution ________________________________________________________________________
page 399 —————————————————...
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This note was uploaded on 03/11/2014 for the course MA 303 taught by Professor Staff during the Spring '08 term at Purdue.
 Spring '08
 Staff

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