Unformatted text preview: initial conditions, we obtain the system of equations Hence and , and the solution of the IVP is
x . . Both functions are monotone increasing. It is easy to show that
and
provided that
31 . For , solution of the ODE requires that
. The characteristic equation is
. With , with roots
and
, the system of equations reduces to . The corresponding eigenvector is Substitution ________________________________________________________________________
page 379 —————————————————————————— CHAPTER 7. ——
of results in the equation . An eigenvector is The general solution is
x
The eigenvalues are distinct and both
. For The equilibrium point is a stable node. , the characteristic equation is given by
and
. With reduces to , with roots
, the system of equations . The corresponding eigenvector is Substitution of results in the equation is . An eigenvector The general solution is
x The eigenvalues are of opposite sign, hence the equilibrium point is a saddle...
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 Spring '08
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 Linear Algebra, eigenvector

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