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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''+2y'-y=t-1et

Short Answer

Expert verified

No, the method of undetermined coefficients can鈥檛 be applied.

Step by step solution

01

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

Given equation,

y''+2y'-y=t-1et

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.

02

Final conclusion.

The R.H.S. of the equationt-1et 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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Most popular questions from this chapter

If Fext(t)=0, equation (3) becomes my''+by'+ky=0. For this equation, verify the following:

(a) If y(t)is a solution so is cy(t), for any constant c.

(b) Ify1(t)andy2(t)are solutions, so is their sum y1(t)+y2(t).

Question: Find a synchronous solution of the form 础肠辞蝉惟迟+叠蝉颈苍惟迟to the given forced oscillator equation using the method of Example to solve forAand By''+2y'+5y=-50sin5t,惟=5 .

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An 8-kg mass is attached to a spring hanging from the ceiling and allowed to come to rest. Assume that the spring constant is 40 N/m and the damping constant is 3 N/sec. At time t = 0, an external force 2sin2t+蟺4N is applied to the system. Determine the amplitude and frequency of the steady-state solution.
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