MA2132 - HW01

MA2132 - HW01 - Willis Thai MA2132 Worksheet 1 1....

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Willis Thai MA2132 – Worksheet 1 1. Substitute rx e x y = ) ( into 0 4 3 3 = + y y y and determine all values of the constant r for which rx e x y = ) ( is a solution. 3 19 2 1 2 1 2 4 0 ) ( 3 0 4 3 3 ) ( ) ( ) ( 2 3 4 2 2 2 ± = ± = = + = + = = = a ac b b r r r e e re e r e r x y re x y e x y rx rx rx rx rx rx rx 2. Verify that ) ln( ) ( c x x y + = is a solution of the differential equation 1 = y e y . Sketch three typical solutions and then find the particular solution for which . 0 ) 0 ( = y . . . 1 1 1 1 1 ) ( ) ln( ) ( ) ln( D E Q c x e c x x y c x x y c x = = + + = + = + 3. Find a function ) ( x f y = that satisfies x xe dx dy = with initial condition 1 ) 0 ( = y . 2 ) ( 2 0 1 ) 0 ( 0 + = = + = = + = = x x x x x e xe x y C C e y C e xe y dx xe dy 4. Find the position function ) ( t x if the acceleration of an object is given by 4 1 ) ( + = t t a where 1 ) 0 ( = x , 1
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MA2132 - HW01 - Willis Thai MA2132 Worksheet 1 1....

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