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MA2132 - HW04

# MA2132 - HW04 - Willis Thai MA2132 – Worksheet 4 1 Use...

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Unformatted text preview: Willis Thai MA2132 – Worksheet 4 1. Use the method of undetermined coefficients to solve each of the following: a. x x y y 2 ) cos( + = + ′ ′ , 1 ) ( = y , 1 ) ( − = ′ y . x x x x x x y C C y x x x x C x x y C y x x x x C x C x y x x x y D C B A x x D Cx x B x A y y x Bx x Ax x B x A y C x Bx x B x Ax x A y D Cx x Bx x Ax y x C x C y i r r y y p p p p h 2 ) sin( 2 1 ) sin( 3 ) cos( ) ( 3 2 1 ) ( 2 ) cos( 2 1 ) sin( 2 1 ) cos( ) sin( ) ( 1 ) ( 2 ) sin( 2 1 ) sin( ) cos( ) ( 2 ) sin( 2 1 , 2 , , 2 ) cos( ) sin( 2 ) cos( 2 ) cos( ) sin( ) sin( 2 ) cos( 2 ) sin( ) cos( ) cos( ) sin( ) cos( ) sin( ) sin( ) cos( 1 2 2 2 1 2 1 2 1 2 1 2 + + − = − = + = − = ′ + + + + − = ′ = = + + + = + = = = = = + = + + − = + ′ ′ − − − = ′ ′ + − + + = ′ + + + = + = ± = = + = + ′ ′ b. 4 3 2 2 + = − ′ − ′ ′ x y y y . 4 17 2 3 2 2 3 2 2 1 4 17 2 3 2 2 3 4 17 2 3 2 3 2 2 2 2 2 1 2 1 2 ) ( , , 4 3 ) 2 2 ( ) 2 2 ( 2 2 2 2 1 , 2 ) 1 )( 2 ( 2 2 − + − + = − + − = − = = − = + = − − + − − + − = − ′ − ′ ′ = ′ ′ + = ′ + + = + = − = = = + − = − − = − ′ − ′ ′ − − x x e C e C x y x x y C B A x C B A x B A Ax y y y A y B Ax y C Bx Ax y e C e C y r r r r r r y y y x x p p p p x x h Willis Thai MA2132 – Worksheet 4 c. ) cos( 4 4 4 2 x e y y y x + = + ′ + ′ ′ − . ) cos( ) sin( 2 ) ( ) cos( ) sin( 2 1 4 3 4 3 2 ) cos( 4 ) cos( 4 ) cos( 3 ) sin( 4 ) sin( 3 2 4 4 ) cos( ) sin( 4 8 2 ) sin( ) cos( 2 2 ) cos( ) sin( 2 ) 2 ( 4 4 4 4 25 3 25 4 2 2 2 2 2 1 25 3 25 4 2 2 25...
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MA2132 - HW04 - Willis Thai MA2132 – Worksheet 4 1 Use...

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