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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
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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anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Have you seen laplace transforms yet?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Find 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)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0\[x(t) = c_1 e^{\lambda_1 t} e_1 + c_1 e^{\lambda_2 t} e_2\] where e1 and e2 are the eigenvectors we found.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0oh and its c2 not c1 the second time

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0We're not supposed to use eignvectors yet

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0hm? I know they x is a vector.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0I'm sorry I can't come up with another way to do this.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0its cool thanks anyways

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0the 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
 5 years ago
Best ResponseYou've already chosen the best response.0Are you using a textbook. Differential Equations and their applications?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Page 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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