Chapter 4: Q1E (page 180)

Decide whether or not the method of undetermined coefficients can be applied to find a particular solution to the given equation. $y'' + 2 y' - y = t^{- 1} e^{t}$

Short Answer

Expert verified

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

Step by step solution

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

Given equation,

$y'' + 2 y' - y = t^{- 1} e^{t}$

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, or cosine, or products of these functions.

Final conclusion.

The R.H.S. of the equation $t^{- 1} e^{t}$ is not in the form of polynomials, exponentials, sine or cosine, or the product of these t functions.

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

And we know that, $t^{- 1}$ is not a polynomial.

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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Decide whether or not the method of undetermined coefficients can be applied to find a particular solution to the given equation. $y'' + 2 y' - y = t^{- 1} e^{t}$

Short Answer

Step by step solution

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

Final conclusion.

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Decide whether or not the method of undetermined coefficients can be applied to find a particular solution to the given equation. y''+2y'-y=t-1et

Short Answer

Step by step solution

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

Final conclusion.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

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Decide whether or not the method of undetermined coefficients can be applied to find a particular solution to the given equation. $y'' + 2 y' - y = t^{- 1} e^{t}$