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 $y'' + 4 y' + 8 y = 0$

The general solution of the given equation $y'' + 4 y' + 8 y = 0$ is $y (t) = e^{- 2 t} (c_{1} \cos (2 t) + c_{2} \sin (2 t))$ .

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Differentiate the value of y.

Given differential equation is $y'' + 4 y' + 8 y = 0 .$

Let role="math" localid="1654067583036" $y = e^{rt}$

Therefore, we have:

$y' (t) = r e^{rt}$

$y'' (t) = r^{2} e^{rt}$

Step 2: Finding the roots.

Then the auxiliary equation is $r^{2} + 4 r + 8 = 0$

The roots of the auxiliary equation are:

$r = \frac{- 4 \pm \sqrt{4^{2} - 4 \times 1 \times 8}}{2 \times 1} r = \frac{- 4 \pm \sqrt{16 - 32}}{2} r = \frac{- 4 \pm 4 i}{2} r = - 2 \pm 2 i$

Step 3: Final answer.

Therefore, the general solution is:

$y (t) = e^{- 2 \times t} (c_{1} \cos (2 t) + c_{2} \sin (2 t)) y (t) = e^{- 2 t} (c_{1} \cos (2 t) + c_{2} \sin (2 t))$

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Fundamentals Of Differential Equations And Boundary Value Problems

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Short Answer

Find a general solution $y'' + 4 y' + 8 y = 0$

Step by Step Solution

Step 1: Differentiate the value of y.

Step 2: Finding the roots.

Step 3: Final answer.

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Fundamentals Of Differential Equations And Boundary Value Problems

Answers without the blur.

Short Answer

Find a general solution y''+4y'+8y=0

Step by Step Solution

Step 1: Differentiate the value of y.

Step 2: Finding the roots.

Step 3: Final answer.

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Find a general solution $y'' + 4 y' + 8 y = 0$