Chapter 4: Q7E (page 180)

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

Short Answer

Expert verified

Yes, the method of undetermined coefficients can be applied.

Step by step solution

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:

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

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

Short Answer

Step by step solution

Use the method of undetermined coefficients.

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.8z'(x)-2z(x)=3x100e4xcos25x

Short Answer

Step by step solution

Use the method of undetermined coefficients.

Final conclusion.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Theoretical and Mathematical Physics

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Study anywhere. Anytime. Across all devices.

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