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- anonymous

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

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- anonymous

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

- chestercat

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- anonymous

Have you seen laplace transforms yet?

- anonymous

no

- anonymous

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)

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- anonymous

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

- anonymous

oh and its c2 not c1 the second time

- anonymous

We're not supposed to use eignvectors yet

- anonymous

X=x1
x2

- anonymous

I don't see why not.

- anonymous

X'=[x2]
[-x1-x2]

- anonymous

hm? I know they x is a vector.

- anonymous

I'm sorry I can't come up with another way to do this.

- anonymous

its cool thanks anyways

- anonymous

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.

- anonymous

Are you using a textbook. Differential Equations and their applications?

- anonymous

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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