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

Question: In Problems 1 - 30, solve the equation.
$\frac{dx}{dt} = 1 + \cos^{2} (t - x)$

The solution of the given equation is $\tan (t - x) + t = C$ .

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Given information and simplification

Given that, $\frac{dx}{dt} = 1 + \cos^{2} (t - x) \cdot \cdot \cdot \cdot \cdot \cdot (1)$

Evaluate the equation (1).

Let us take $u = t - x$ . Then, $\frac{dx}{dt} = 1 - \frac{du}{dt}$ .

$\begin{matrix} \frac{dx}{dt} = 1 + \cos^{2} (t - x) \\ 1 - \frac{du}{dt} = 1 + \cos^{2} u \\ - \frac{du}{dt} = \cos^{2} u \\ - \frac{1}{\cos^{2} u} du = dt \end{matrix} - \frac{1}{\cos^{2} u} du = dt \cdot \cdot \cdot \cdot \cdot \cdot (2)$

Step 2: Integration

Now integrate the equation (2) on both sides.

$\begin{matrix} - \int \frac{1}{\cos^{2} u} du = \int dt \\ - \int \sec^{2} u du = t + C \\ - \tan u = t + C \end{matrix}$

Substitute the value of u here.

$\tan (t - x) + t = C$

So, the solution is $\tan (t - x) + t = C$

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Fundamentals Of Differential Equations And Boundary Value Problems

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Short Answer

Question: In Problems 1 - 30, solve the equation.
$\frac{dx}{dt} = 1 + \cos^{2} (t - x)$

Step by Step Solution

Step 1: Given information and simplification

Step 2: Integration

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Fundamentals Of Differential Equations And Boundary Value Problems

Answers without the blur.

Short Answer

Question: In Problems 1 - 30, solve the equation. dxdt=1+cos2t-x

Step by Step Solution

Step 1: Given information and simplification

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Question: In Problems 1 - 30, solve the equation.
$\frac{dx}{dt} = 1 + \cos^{2} (t - x)$