Quiz4 - - Let 1 1 1 2 2 1 1 3 3 1 2 2 1 1 1 1 2 2 t t u u u...

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Quiz 4 Find a particular solution to the system of first order differential equations 1 1 2 2 1 2 1 2 1 1 t y y e y y - = + - by the diagonalization method . The matrix 1 2 2 1 A = has eigenvalues 3, 1 λ = - with eigenvectors 1 1       and 1 1 - . Solution: 1 1 1 1 1 1 1 1 1 1 0 1 1 1 0 1 0 1 0 2 2 2 2 1 1 1 1 0 1 0 2 1 1 0 2 0 1 1 1 1 1 2 2 1 1 2 2 1 1 2 2 X X - = →  - - - - - - - = 
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Unformatted text preview: - Let 1 1 1 2 2 1 1 3 3 1 2 2 1 1 1 1 2 2 t t u u u X y u u e u u e--- ′ = ′ = ⇒ = + ⇒ --′ = -+- A solution is 1 2 0, t u u te-= = Hence ( 29 1 1 1 1 1 1 t p t y Xu te te-- = = = --...
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This note was uploaded on 09/05/2011 for the course EGM 4313 taught by Professor Mei during the Spring '08 term at University of Florida.

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