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. $x'' + 5 x' - 3 x = 3^{t}$

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 logarithms properties for simplification of the given differential equation.

Given equation,

$x'' + 5 x' - 3 x = 3^{t}$

Simplify the above equation by using logarithms properties,

$\begin{matrix} x'' + 5 x' - 3 x = e^{\ln (3^{t})} \\ x'' + 5 x' - 3 x = e^{t [\ln (3)]} \\ x'' + 5 x' - 3 x = e^{[\ln (3)] t} \end{matrix}$

Step 2: Use the method of undetermined coefficients to find a particular solution of a given differential equation.

The given differential equation is in the form of;

$ax'' + bx' + cx = e^{rt}$

According to the method of undetermined coefficients,

To find a particular solution to the differential equation;

$ay'' (x) + by' (x) + cy (x) = {Ct}^{m} e^{rt}$

Where m is a non-negative integer, use the form;

$y_{p} (x) = t^{s} (A_{m} t^{m} + . .. + A_{1} t + A_{0}) e^{rt}$

Compare with the given differential equation,

$x'' + 5 x' - 3 x = e^{[\ln (3)] t}$

Condition satisfies,

s = 1 if r is a simple root of the associated auxiliary equation.

Therefore, the particular solution of the equation,

$y_{p} (x) = {Ate}^{\ln (3) t}$

So, 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. $x'' + 5 x' - 3 x = 3^{t}$

Step by Step Solution

Step 1: Use logarithms properties for simplification of the given differential equation.

Step 2: Use the method of undetermined coefficients to find a particular solution of a given differential equation.

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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. x''+5x'-3x=3t

Step by Step Solution

Step 1: Use logarithms properties for simplification of the given differential equation.

Step 2: Use the method of undetermined coefficients to find a particular solution of a given differential equation.

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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. $x'' + 5 x' - 3 x = 3^{t}$