WrittenHW07-Solutions

WrittenHW07-Solutions - Math 216 (Section 50) Written...

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Unformatted text preview: Math 216 (Section 50) Written Homework #7 – Solutions Fall 2007 1 ( 4.1–4 ) Let us first rewrite x (3)- 2 t x 00 + 1 t 2 x + 5 t 3 x = ln t t 3 . Let us define x 1 := x, x 2 := x = x 1 , x 3 := x 00 = x 2 . Therefore the given differential equations are rewritten as follows: x 1 = x 2 x 2 = x 3 x 3- 2 t x 3 + 1 t 2 x 2 + 5 t 3 x 1 = ln t t 3 = ⇒ x 1 = x 2 x 2 = x 3 x 3 = 2 t x 3- 1 t 2 x 2- 5 t 3 x 1 + ln t t 3 . 2 ( 4.1–8 ) Let us define x 1 := x, x 2 := x = x 1 , y 1 := y, y 2 := y = y 1 . Note that then x 00 = x 2 and y 00 = y 2 . Therefore the given system of differential equations are rewritten as follows: x 00 + 3 x + 4 x- 2 y = 0 y 00 + 2 y- 3 x + y = cos t = ⇒ x 1 = x 2 y 1 = y 2 x 2 + 3 x 2 + 4 x 1- 2 y 1 = 0 x 2 + 2 y 2- 3 x 1 + y 1 = cos t = ⇒ x 1 = x 2 y 1 = y 2 x 2 =- 3 x 2- 4 x 1 + 2 y 1 y 2 =- 2 y 2 + 3 x 1- y 1 + cos t 3 ( 4.1–9 ) Let us define x 1 := x, x 2 := x = x 1 , y 1 := y, y 2 := y = y 1 . z 1 := z, z 2 := z = z 1 . Note that then x 00 = x 2 , y 00 = y 2 , and z 00 = z 2 . Therefore the given system of differential equations are rewritten as follows: x 00 = 3 x- y + 2 z y 00 = x + y- 4 z z 00 = 5 x- y- z = ⇒ x 1 = x 2 y 1 = y 2 z 1 = z 2 x 2 = 3 x 1- y 1 + 2 z 1 y 2 = x 1 + y 1- 4 z 1 z 2 = 5 x 1- y 1- z 1 1 4 ( 4.1–16 ) Given x = 8 y and y =- 2 x , x 00...
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This homework help was uploaded on 04/02/2008 for the course ENGR 101 taught by Professor Ringenberg during the Fall '07 term at University of Michigan.

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WrittenHW07-Solutions - Math 216 (Section 50) Written...

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