Science & engineering math: integro-differential equation

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Homework Help Overview

The problem involves an integro-differential equation that appears to relate to convolution, specifically involving the functions y'(u) and y(t-u). The integral is defined from t to 0, with an initial condition y(0) = 0.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the nature of the problem, questioning whether it truly represents a convolution due to the presence of y' and y. There are attempts to relate the problem to Laplace transforms and the properties of convolution.

Discussion Status

Some participants have suggested taking the Laplace transform of both sides of the equation as a potential starting point. There is an ongoing exploration of how to approach the problem, with some expressing confusion about the initial steps.

Contextual Notes

Participants are considering the implications of the initial condition and the specific forms of the functions involved, as well as the definitions and properties of convolution in the context of the problem.

chatterbug219
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Homework Statement



[itex]\int[/itex] y'(u)y(t-u)du = 24t3
The integral goes from t (top) to 0 (bottom)
With y(0) = 0

Homework Equations



I want to say it kind of looks like a convolution problem
[itex]\int[/itex] f(u)g(t-u)du
The integral goes from t (top) to 0 (bottom)

The Attempt at a Solution


I have no idea...
 
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When you see a convolution in a homework problem, you should immediately think of a transform that reduces it to a multiplication. This transform can even handle the derivative easily...
 
Well if it is convolution then it would just be
F(s)*G(s)
But I was more concerned about whether or not it actually was convolution. Because its y' and y, and those are both completely different, then it would be convolution then?
So I would need to take the Integral of y'(u) and y(t-u) then? And the integral of 24t3?
 
it is a convolution between to functions, i.e., y'(t) and y(t), their Laplace transform are related, because one is the derivative of the other. So there is only one F(s) to solve for, the other is simply related to this one.
 
Okay, understandable...but how do I start the problem? I'm still confused about how to start...
 
chatterbug219 said:
Okay, understandable...but how do I start the problem? I'm still confused about how to start...

What is the Laplace transform of a convolution?

RGV
 
F(s)G(s)
 
So "start" by taking the Laplace transform of both sides!
 

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