s11_mthsc208_hw11

s11_mthsc208_hw11 - MthSc 208 Fall 2011(Differential...

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Unformatted text preview: MthSc 208, Fall 2011 (Differential Equations) Dr. Matthew Macauley HW 11 Due Monday March 7th, 2011 (1) Solve the following differential equations (a) y = 9 y (b) y 00 = 9 y (c) y 00 =- 9 y (d) y 00 =- 9 y + 4. (2) State whether the given system is autonomous or nonautonomous, and also whether it is homogeneous or inhomogeneous. (a) x = y, y = x + 4 (b) x = x + 2 y + sin t, y =- x + y- cos t (c) x =- 2 tx + y y = 3 x- y (d) x = x + 2 y + 4 , y =- 2 x + y- 3 (e) x = 3 x- y, y = x + 2 y (f) x =- x + ty, y = tx- y (g) x = x + y + 4 , y =- 2 x + (sin t ) y (h) x = 3 x- 4 y, y = x + 3 y (3) Transform the given 2 nd initial value problem into an initial value problem of two 1 st order equations (by letting x 1 = u and x 2 = u ), and write it in matrix form: x = Ax + b , x ( t ) = x . (No need to solve!) (a) u 00 + 0 . 25 u + 4 u = 2cos3 t, u (0) = 1 , u (0) =- 2 (b) tu 00 + u + tu = 0 , u (1) = 1 , u (1) = 0 (4) In each problem below, an inhomogeneous system x = Ax + b of two first order ODEs is...
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This note was uploaded on 03/11/2012 for the course MTHSC 208 taught by Professor Staufeneger during the Spring '09 term at Clemson.

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s11_mthsc208_hw11 - MthSc 208 Fall 2011(Differential...

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