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 to the given differential equation. $u'' + 11 u = 0$

$u = c_{1} \cos (\sqrt{11} t) + c_{2} \sin (\sqrt{11} t)$

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Complex conjugate roots.

If the auxiliary equation has complex conjugate roots, then the general solution is given as: $y (t) = c_{1} e^{α t} c o s β t + c_{2} e^{α t} s i n β t$

Step 2: Write the auxiliary equation of the given differential equation

The differential equation is, $u'' + 11 u = 0$

The auxiliary equation for the above equation, $m^{2} + 11 = 0$

Step 3: Find the roots of the auxiliary equation.

Solve the auxiliary equation,

$\begin{matrix} m^{2} + 11 = 0 \\ m^{2} = - 11 \\ m = \pm i \sqrt{11} \end{matrix}$

The roots of the auxiliary equation are, $m_{1} = i \sqrt{11}, & m_{2} = - i \sqrt{11} .$

The general solution of the given equation is $u = c_{1} \cos (\sqrt{11} t) + c_{2} \sin (\sqrt{11} t) .$

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Fundamentals Of Differential Equations And Boundary Value Problems

Answers without the blur.

Short Answer

Find a general solution to the given differential equation. $u'' + 11 u = 0$

Step by Step Solution

Step 1: Complex conjugate roots.

Step 2: Write the auxiliary equation of the given differential equation

Step 3: Find the roots of the auxiliary equation.

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Fundamentals Of Differential Equations And Boundary Value Problems

Answers without the blur.

Short Answer

Find a general solution to the given differential equation.u''+11u=0

Step by Step Solution

Step 1: Complex conjugate roots.

Step 2: Write the auxiliary equation of the given differential equation

Step 3: Find the roots of the auxiliary equation.

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Find a general solution to the given differential equation. $u'' + 11 u = 0$