# The roots of the characteristic equation are setting

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Unformatted text preview: point. 32. The system of differential equations is Solution of the system requires analysis of the eigenvalue problem . The characteristic equation is , with roots and . With , the equations reduce to . A corresponding eigenvector is given by Setting , the system reduces to the equation . An eigenvector is Hence the general solution is The eigenvalues are distinct and both We find that the equilibrium point is a stable node. Hence all solutions converge to 33 . Solution of the ODE requires analysis of the algebraic equations ________________________________________________________________________ page 380 —————————————————————————— CHAPTER 7. —— . The characteristic equation is The eigenvectors are real and distinct, provided that the discriminant is positive. That is, , which simplifies to the condition . . The parameters in the ODE are all positive. Observe that the sum of the roots is Also, the product of the roots is It follows that both roots are negative. Hen...
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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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