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. $y'' (θ) + 3 y' (θ) - y (θ) = secθ$

No, the method of undetermined coefficients can’t be applied.

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Use the method of undetermined coefficients.

Given equation,

$y'' (θ) + 3 y' (θ) - y (θ) = secθ$

Here, the given differential equation is non-homogeneous.

According to the method of undetermined coefficients, the method of undetermined coefficients applies only to non-homogeneities that are polynomials, exponentials, sines, or cosines, or products of these functions.

Step 2: Final conclusion

The given differential equation is in the form of;

$ay'' + by' + cy = g (t)$

Compare with the given differential equation,

We get,

$g (t) = secθ$

We know that, $secθ$ is not a linear combination of the term of the form of polynomials, exponentials, sine or cosine, or product of these t functions.

Therefore, the method of undetermined coefficients cannot 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. $y'' (θ) + 3 y' (θ) - y (θ) = secθ$

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.y''(θ)+3y'(θ)-y(θ)=secθ

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. $y'' (θ) + 3 y' (θ) - y (θ) = secθ$