Understanding the Inverse Laplace Transform of Fractional Expressions

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Homework Help Overview

The discussion revolves around finding the inverse Laplace transform of the expression (5/((2x+3)(4+x^2))). Participants are exploring the implications of the terms in the denominator and their effects on the resulting inverse transform.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • The original poster attempts to understand why the solution includes trigonometric terms despite their expectation based on Laplace tables. Some participants question the necessity of performing partial fraction expansion (PFE) and how it relates to the presence of squared variables in the denominator.

Discussion Status

Participants are actively discussing the steps involved in the partial fraction expansion and its implications for the inverse transform. There is recognition of the need for a more complex residual term in the PFE, indicating a productive exploration of the problem.

Contextual Notes

There is mention of potential confusion regarding the conditions under which trigonometric terms appear in the solution, as well as the specific form of the residual needed for the PFE. Participants are navigating these assumptions without reaching a definitive conclusion.

Ry122
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Homework Statement



I'm attempting to find the inverse laplace transform of (5/((2x+3)(4+x^2)))

The Attempt at a Solution



Here's the solution:
http://www.wolframalpha.com/input/?i=inverse+laplace+transform+(5/((2x+3)(4+x^2)))

There's 3 terms in the solution and 2 are trigonometric. But according to laplace tables you
only get a trigonometric term if a variable in one of the terms of the denominator is squared and if you perform PFE there won't be any variables squared so I'm not sure what's going on here.
 
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Did you actually do the partial fractions expansion?
 
susskind_leon said:

How do you work out that term for the PFE?
Using this method I got the correct answer for the 2nd term but not the term with x^2 as the denominator.

4+x^2 = 0
so the limit is at x = 2

sub x = 2 into
5/(2x+3) to get the value of the residual then
the final answer is 5/7(4+x^2)
 
Worked it out, I needed Bx + C as the residual and not just B.
 

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