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 $y'' - 3 y' - 11 y = 0$

The general solution of the given equation $y'' - 3 y' - 11 y = 0$ is $y (t) = c_{1} e^{^{\frac{(3 + \sqrt{53}) t}{}}} + c_{2} e^{\frac{(3 - \sqrt{53}) t}{}}$ .

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Given information.

The differential equation is $y'' - 3 y' - 11 y = 0 .$

Step 2: Finding roots of the auxiliary equation.

Then the auxiliary equation is $r^{2} - 3 r - 11 = 0 .$

The roots of the auxiliary equation are:

$\begin{matrix} r = \frac{3 \pm \sqrt{3^{2} - 4 \times - 11 \times 1}}{2 \times 1} \\ r = \frac{3 \pm \sqrt{9 + 44}}{2} \\ r = \frac{3 \pm \sqrt{53}}{2} \end{matrix}$

Step 3: Final answer.

Therefore, the general solution is:

$y (t) = c_{1} e^{^{\frac{(3 + \sqrt{53}) t}{2}}} + c_{2} e^{\frac{(3 - \sqrt{53}) t}{2}}$

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Fundamentals Of Differential Equations And Boundary Value Problems

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Short Answer

Find a general solution $y'' - 3 y' - 11 y = 0$

Step by Step Solution

Step 1: Given information.

Step 2: Finding roots of the auxiliary equation.

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''-3y'-11y=0

Step by Step Solution

Step 1: Given information.

Step 2: Finding roots of the auxiliary equation.

Step 3: Final answer.

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Find a general solution $y'' - 3 y' - 11 y = 0$