quiz 8 - and writing the general solution. ~ ,v. ..u-~...

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Fall 2008 Math 285 Quiz 8: Nav 14 Name: If you cannot complete a problem (perhaps because you forgot a formula) but you think you know how, please describe. Correct methods will receive partial credits. 1. Answer the following questions regarding the system of homogeneous ODEs X' = (~ ~) X (a) Given that Al = 3 is an eigenvalue of the matrix above with corresponding eigenvector K1 = (~), write a solution of the system corresponding to this eigenpair. X\ ~ (: Je;t (b) Completely solve the system of equations by finding the other eigenpair,
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Unformatted text preview: and writing the general solution. ~ ,v. ..u-~ ""t l L I) '=- () 0: S Ov\ e.. - v ~\ v-L .~ Cor-f'.-t-<:; ~. e.-vz. .(w \ ;\ be. ." ,:>",\/\ Q", Xl~) ~L \ \ e,-t Cz. _,-. 2. Solve the system of nonhomogeneous ODEs X' = (3 1 X + (~2) using the variation of parameters formula Xp = ~(t) J ~-I(t)F(t)dt with (a) Write the matrices ~(t) and ~-l(t). ::.(C.4"t e--LlJ-\ <f> "t:-L""t.' k:.-e'"-E:-. / ~ X (1) 4t ( 1)-2t 1 = 1 e and X2 =-1 e...
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