Book edition 9th

Author(s) R. Kent Nagle, Edward B. Saff, Arthur David Snider

Pages 616 pages

ISBN 9780321977069

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Short Answer

use the annihilator method to determinethe form of a particular solution for the given equation.
$y''' + 2 y'' - y' - 2 y = e^{x} - 1$

$y_{p} (x) = c_{1} + c_{5} x e^{x}$

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Solve the homogeneous of the given equation

The homogeneous of the given equation is

$(D^{3} + 2 D^{2} - D - 2) [y] = 0$

The solution of the homogeneous is

$y_{h} (x) = c_{1} e^{- 2 x} + c_{2} e^{- x} + c_{3} e^{x}$ (1)

Now $e^{x} - 1$ is annihilated by $(D^{2} - D)$

Then, every solution to the given nonhomogeneous equation also satisfies

. $(D^{2} - D)$ $(D^{3} + 2 D^{2} - D - 2) [y] = 0$

Then

$y (x) = c_{1} + c_{2} e^{- 2 x} + c_{3} e^{- x} + c_{4} e^{x} + c_{5} x e^{x}$ (2)

is the general solution to this homogeneous equation

We know $u (x) = u_{h} + u_{p}$

Comparing (1) & (2)

$y_{p} (x) = c_{1} + c_{5} x e^{x}$

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Fundamentals Of Differential Equations And Boundary Value Problems

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Short Answer

use the annihilator method to determinethe form of a particular solution for the given equation.
$y''' + 2 y'' - y' - 2 y = e^{x} - 1$

Step by Step Solution

Step 1: Solve the homogeneous of the given equation

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Fundamentals Of Differential Equations And Boundary Value Problems

Answers without the blur.

Short Answer

use the annihilator method to determinethe form of a particular solution for the given equation.y'''+2y''-y'-2y=ex-1

Step by Step Solution

Step 1: Solve the homogeneous of the given equation

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use the annihilator method to determinethe form of a particular solution for the given equation.
$y''' + 2 y'' - y' - 2 y = e^{x} - 1$