Short Answer

Decide whether the method of undetermined coefficients together with superposition can be applied to find a particular solution of the given equation. Do not solve the equation. $y'' - 6 y' - 4 y = 4 \sin 3 t - t^{2} e^{3 t} + \frac{1}{t}$

No, the method of undetermined coefficients together with superposition can’t 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,

$y'' - 6 y' - 4 y = 4 \sin 3 t - t^{2} e^{3 t} + \frac{1}{t}$

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, sine, cosine, or products of these functions.

Step 2: Conclusion

The given R.H.S. of the equation $\frac{1}{t}$ is not the combination of polynomials t.

From the definition of a polynomial, it should have only non-negative integers as powers.

Therefore, it is not a product of a polynomial and an exponential function.

So, 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 the method of undetermined coefficients together with superposition can be applied to find a particular solution of the given equation. Do not solve the equation. $y'' - 6 y' - 4 y = 4 \sin 3 t - t^{2} e^{3 t} + \frac{1}{t}$

Step by Step Solution

Step 1: Use the method of undetermined coefficients

Step 2: Conclusion

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Fundamentals Of Differential Equations And Boundary Value Problems

Answers without the blur.

Short Answer

Decide whether the method of undetermined coefficients together with superposition can be applied to find a particular solution of the given equation. Do not solve the equation.y''-6y'-4y=4sin3t-t2e3t+1t

Step by Step Solution

Step 1: Use the method of undetermined coefficients

Step 2: Conclusion

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Decide whether the method of undetermined coefficients together with superposition can be applied to find a particular solution of the given equation. Do not solve the equation. $y'' - 6 y' - 4 y = 4 \sin 3 t - t^{2} e^{3 t} + \frac{1}{t}$