# The general solution found in prob section is given

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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 complex-valued 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 complex-valued 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.

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