eng math 501e_2011 2012 fall_week2_applications

eng math 501e_2011 2012 fall_week2_applications - 1...

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Unformatted text preview: 1 Application 1 (Reduction of order – How to obtain a second solution) ( ) 2 1 1 '' 2 ' 2 0 has y as a first solution. Find another independent solution. x y xy y x-- + = = Solution ( ) 2 2 2 2 2 2 2 2 ( 1) 2 2 1 2 2 ' side x 1 , 2 2 '' ' 1 1 '' ( ) ' ( ) ( ) 2 2 ( ) 1 1 1 , 2 ( 1) 1 1 . . 1 .( 1) pdx In x Let s divide each by x y y y x x y P x y q x y r x x x P x pdx dx x x t x dt xdx dt In t In x t U e U e y x U x x---- + =-- + + = = - → - =-- =- = = =- ∫ = → = → =- ∫ ∫ ∫ 2 2 2 2 1 2 1 1 1 1 1- 1 . 1 U x u Udx dx x x x y u y x x y x x → = -   = = = +       = = + → = +     ∫ ∫ 1 1 2 2 1 2 2 1 1 2 2 1 1 2 1 2 Note: ( ) ( ) ( 0 and 0) or ( ) k y x k y x k k k k y y y y k k y and y are proportional linearly dependent + = ≠ ≠ = - = - Application 2 (Homogeneous equations with constant coefficients – Two distinct real roots) Solve the initial value problem....
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This note was uploaded on 12/04/2011 for the course TRADE 1056596 taught by Professor Ayladinç during the Spring '11 term at Istanbul Bilgi University.

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eng math 501e_2011 2012 fall_week2_applications - 1...

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