(2D5 – 7D* + 2D³ + 3D²)(f) = 0 -

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Determine the general/or particular solutions of the following linear ordinary differential equations .Show complete solutions.

(2D5 – 7Dª + 2D³ + 3D²)(f) = 0
(D² – 16)(D² – 4D + 4)(D² – 4D + 1)(f) = 0
Hint: You can use the quadratic formula; if not factorable
Determine the u(x) from (D³ – 3D² + 3D – 1)(f) = 0 that will satisfy the following
initial condition:
u(0) = 2
D(u(0)) = 1
%3D
D²(u(0)) = -2
(D² – 4D + 4)() = 4 – 6e3x
%3D
(D + 3)2(f) = 12x²e2x + 6xe2x –- 3e2x
%3D
Transcribed Image Text:(2D5 – 7Dª + 2D³ + 3D²)(f) = 0 (D² – 16)(D² – 4D + 4)(D² – 4D + 1)(f) = 0 Hint: You can use the quadratic formula; if not factorable Determine the u(x) from (D³ – 3D² + 3D – 1)(f) = 0 that will satisfy the following initial condition: u(0) = 2 D(u(0)) = 1 %3D D²(u(0)) = -2 (D² – 4D + 4)() = 4 – 6e3x %3D (D + 3)2(f) = 12x²e2x + 6xe2x –- 3e2x %3D
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