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anonymous

  • 5 years ago

Find a basis for the set of solutions of the given differential equation: x'=|0 1 | x |-1 -1|

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  1. anonymous
    • 5 years ago
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    Have you seen laplace transforms yet?

  2. anonymous
    • 5 years ago
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    no

  3. anonymous
    • 5 years ago
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    Find the eigenvalues of the matrix. Use the characteristic polynomial. Use the eigenvalues to find the eigenvectors. (I am assuming you know linear algebra, if you are in a differential course)

  4. anonymous
    • 5 years ago
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    \[x(t) = c_1 e^{\lambda_1 t} e_1 + c_1 e^{\lambda_2 t} e_2\] where e1 and e2 are the eigenvectors we found.

  5. anonymous
    • 5 years ago
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    oh and its c2 not c1 the second time

  6. anonymous
    • 5 years ago
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    We're not supposed to use eignvectors yet

  7. anonymous
    • 5 years ago
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    X=x1 x2

  8. anonymous
    • 5 years ago
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    I don't see why not.

  9. anonymous
    • 5 years ago
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    X'=[x2] [-x1-x2]

  10. anonymous
    • 5 years ago
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    hm? I know they x is a vector.

  11. anonymous
    • 5 years ago
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    I'm sorry I can't come up with another way to do this.

  12. anonymous
    • 5 years ago
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    its cool thanks anyways

  13. anonymous
    • 5 years ago
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    the basis for the matrix is (1,0) (0,1) I don't know how to relate it to the solution which is of the form I gave above. But you NEED to know the eigenvalues. e1 and e2 can be any ol' basis vectors.

  14. anonymous
    • 5 years ago
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    Are you using a textbook. Differential Equations and their applications?

  15. anonymous
    • 5 years ago
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    Page 294 has an example really similar to yours. I can't see the entire book online. It's on google books, if you don't have a hard copy.

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