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eng math 501e_2011 2012 fall_week3_applications

eng math 501e_2011 2012 fall_week3_applications -...

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1 Application 1 (Non homogeneous high order dif. equ.) Solve the following differential equation. 2 2 2 ''' 3 '' 3 4sin ıv x y y y x e x + - = + + Solution 2 2 4 3 2 2 2 2 1 2 3 4 3 1 1 2 3 4 4 3 2 21 3 2 21 2 21 21 21 24 2(24 6 ) 3(12 6 2 ) 2 3 0 ( 2 3) 0 ( 3)( 1) 0 0 , 1 , 3 ' 4 3 2 '' 12 6 2 ''' 24 6 24 24 x x ıv a ax b ax bx c x r r r r r r r r r r r r r y c c x c e c e y ax bx cx dx e y ax bx cx d y ax bx c y ax b y a - + + - + + = + - = + - = + - = = = = = - = + + + = + + + + = + + + = + + = + = 2 2 4 3 2 21 48 12 36 18 6 1 36 1 48 18 0 48. 18 36 2 27 24 12 6 0 1 2 7 24. 12. 6 36 27 27 1 2 7 36 27 27 a ax b ax bx c x a a b b b a b c c c y x x x + + - - - = = - - = - = = - + - = - + - = = - = - - - 2 22 2 22 2 22 2 22 2 22 . ' 2 . '' 4 . ''' 8 . 16 . x x x x ıv x y K e y K e y K e y K e y K e = = = = = 2 2 2 2 2 22 23 23 23 23 23 16 . 2.8 . 3.4 . 3. 3 20 3 20 3 . 20 .sin .cos ' .cos .sin '' .sin .cos ''' .cos .sin .sin .cos .sin .cos 2( .cos .sin ) 3( .sin .c x x x x x ıv K e K e K e e K K y e y x x y x x y x x y x x y x x x x x x x α β α β α β α β α β α β α β α β + - = = = = = + = - = - - = - + = + + + - + - - - 23 1 21 22 23 3 4 3 2 1 2 3 4 os ) 4sin .sin .cos 2 .cos 2 .sin 3 .sin 3 .cos 4sin 2 3 4 2 3 0
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