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Unformatted text preview: olution may be written as
x 7. Solution of the ODE requires analysis of the algebraic equations
For a nonzero solution, we must have
. The only root
, which is an eigenvalue of multiplicity two. Substituting
coefficient matrix, the system reduces to the single equation
. Hence the
corresponding eigenvector is
One solution is
x . For a second linearly independent solution, we search for a generalized eigenvector.
Its components satisfy ________________________________________________________________________
page 416 ————————————————————————— CHAPTER 7. —— ,
, some arbitrary constant. Then
It follows that a second solution is given by
x Dropping the last term, the general solution is
Imposing the initial conditions, we require that ,
which results in and Therefore the solution of the IVP is
page 417 —————————————————————————— CHAPTER 7. —...
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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