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

Decide whether or not the method of undetermined coefficients can be applied to find a particular solution of the given equation. $8 z' (x) - 2 z (x) = 3 x^{100} e^{4 x} \cos 25 x$

Yes, the method of undetermined coefficients can be applied.

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Use the method of undetermined coefficients.

Given equation,

$8 z' (x) - 2 z (x) = 3 x^{100} e^{4 x} \cos 25 x . .... (1)$

According to the method of undetermined coefficients,

To find a particular solution to the differential equation;

$ay'' + by' + cy = \{\begin{array}{l} {Ct}^{m} e^{αt} cosβt \\ or \\ {Ct}^{m} e^{αt} sinβt \end{array}\}$

For, $β \neq 0$ use the form:

$y_{p} (x) = t^{s} (A_{m} t^{m} + . .. + A_{1} t + A_{0}) e^{αt} cosβt + t^{s} (B_{m} t^{m} + . .. + B_{1} t + B_{0}) e^{αt} sinβt$

Step 2: Final conclusion.

Compare with the given differential equation,

$8 z' (x) - 2 z (x) = 3 x^{100} e^{4 x} \cos 25 x$

We have,

$β = 25 \neq 0$

Therefore, the method of undetermined coefficients can be applied.

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Fundamentals Of Differential Equations And Boundary Value Problems

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Short Answer

Decide whether or not the method of undetermined coefficients can be applied to find a particular solution of the given equation. $8 z' (x) - 2 z (x) = 3 x^{100} e^{4 x} \cos 25 x$

Step by Step Solution

Step 1: Use the method of undetermined coefficients.

Step 2: Final conclusion.

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Fundamentals Of Differential Equations And Boundary Value Problems

Answers without the blur.

Short Answer

Decide whether or not the method of undetermined coefficients can be applied to find a particular solution of the given equation.8z'(x)-2z(x)=3x100e4xcos25x

Step by Step Solution

Step 1: Use the method of undetermined coefficients.

Step 2: Final conclusion.

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Decide whether or not the method of undetermined coefficients can be applied to find a particular solution of the given equation. $8 z' (x) - 2 z (x) = 3 x^{100} e^{4 x} \cos 25 x$