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

Find a general solution for the differential equation with x as the independent variable.
$y''' - 3 y'' - y' + 3 y = 0$

Thus, the general solution to the given differential equation is; $y = C_{1} e^{3 x} + C_{2} e^{x} + C_{3} e^{- x}$

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Find the auxiliary equation

The given differential equation is;

$y''' - 3 y'' - y' + 3 y = 0$

The auxiliary equation is,

$m^{3} - 3 m^{2} - m + 3 = 0$

Take a fraction of the above equation,

$\begin{matrix} m^{2} (m - 3) - 1 (m - 3) = 0 \\ (m - 3) (m^{2} - 1) = 0 \\ m_{1} = 3, m_{2} = 1, m_{3} = - 1 \end{matrix}$

Step 2: Write the general solution

The roots are real and distinct; therefore the general solution to the given differential equation is given as:

$\begin{matrix} y = C_{1} e^{m_{1} x} + C_{2} e^{m_{2} x} + C_{3} e^{m_{3} x} \\ y = C_{1} e^{(3) x} + C_{2} e^{(1) x} + C_{3} e^{(- 1) x} \\ y = C_{1} e^{3 x} + C_{2} e^{x} + C_{3} e^{- x} \end{matrix}$

Thus, the general solution to the given differential equation is;

$y = C_{1} e^{3 x} + C_{2} e^{x} + C_{3} e^{- x}$

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Fundamentals Of Differential Equations And Boundary Value Problems

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Short Answer

Find a general solution for the differential equation with x as the independent variable.
$y''' - 3 y'' - y' + 3 y = 0$

Step by Step Solution

Step 1: Find the auxiliary equation

Step 2: Write the general solution

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Fundamentals Of Differential Equations And Boundary Value Problems

Answers without the blur.

Short Answer

Find a general solution for the differential equation with x as the independent variable.y'''-3y''-y'+3y=0

Step by Step Solution

Step 1: Find the auxiliary equation

Step 2: Write the general solution

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Find a general solution for the differential equation with x as the independent variable.
$y''' - 3 y'' - y' + 3 y = 0$