HW 11 - D ) is a polynomial differential operator and if...

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MATH 225 HOMEWORK 11 pp. 458 – 459 #5, 6, 13, 14, 16, 18, 29, 43 pp. 468 – 470 #10 – 13, 17, 18, 22, 24, 27, 32 – 35, 41, 43 pp. 480 – 481 #7 – 10, 14, 17, 19, 20, 26, 27, 36 – 38 p. 512 #2, 11, 19 – 21, 30 A. Let Ly = F ( x ) be an n -th order LDE with F ( x ) 0. i) Show that there are n + 1 linearly independent solutions of Ly = F ( x ). ii) Show that any n + 2 solutions of Ly = F ( x ) must be linearly dependent. B. Solve the IVP: x 2 y ' + y = 2 with y (1) = 3. C. Solve the IVP: y ' + y = sin ( x ) with y (0) = 1. D. Find the general solution of ( D 8 – 5 D 4 + 4 I ) y = 0. E. Find all common solutions of the differential equations f [4] f = 0 and f [4] – 3 f [3] + 2 f [2] = 0 and verify that your answer is correct. F. If p (
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Unformatted text preview: D ) is a polynomial differential operator and if for all polynomials g ( x ) and q ( x ) of degrees six or less g ( x ) sin ( x ) and q ( x ) cos ( x ) e-2 x are solutions of p ( D ) y = 0, find p ( x ) of least degree. G. Find a polynomial differential operator p ( D ) of least degree whose kernel contains the functions sin ( x ), xcos ( x ), cos (2 x ) e x , and x 2 sin (3 x ) e-2 x . H. Find the general solution of f " f = e 2 x 1 + e 2 x . I. Find the general solution of f ''' + 6 f " + 11 f ' + 6 f = 1 1 + e x . Hand In 11A) pp. 468-470 #22; 24; 27; 34; p. 481 #14; 20; 26; p. 512 #11; 19; C 11B) p. 470 #41; A; D; I Due Monday November 21...
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