Solve Input Math Problem: y``+y`+y=r(t)

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Homework Help Overview

The discussion revolves around the differential equation y'' + y' + y = r(t), focusing on the role of r(t) as the input function and its relationship to the variable t.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants explore why r(t) is considered the input rather than t itself, with some emphasizing that r(t) represents a general function of t. Others discuss the interpretation of differential equations in engineering terms, likening them to a machine that processes inputs to produce outputs.

Discussion Status

The conversation includes various interpretations of the equation and its components. Some participants have provided clarifications regarding the terminology used, while others have expressed differing views on the mathematical versus engineering perspectives.

Contextual Notes

There is an ongoing exploration of the definitions and roles of the terms within the equation, particularly the distinction between input and output in the context of differential equations.

asdf1
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y`` +y`+y=r(t)
why's r(t) the input and not t?
 
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asdf1 said:
y`` +y`+y=r(t)
why's r(t) the input and not t?

Because the right hand side of that equation denotes a function of t.

r(t) could be t but it can also be every other function that depends on t.

Basically, r(t) is the most general form to denote "a function of t"

marlon
 
That's not really mathematics- it's "Engineer speak".

From the point of view of an Engineer, a differential equation is a machine to which you supply an "input" and get an "output". The differential operator y"+ y'+ y is the machine. Whatever function you have on the right hand side is the "input" (which varies with t) and y(t) satisfying the equation is the "output".

(Edited- thanks, Marlon.)
 
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HallsofIvy said:
That's not really mathematics- it's "Engineer speak".
From the point of view of an Engineer, a differential equation is a machine to which you supply an "input" and get an "output". The differential operator y"+ y' is the machine. Whatever function you have on the right hand side is the "input" (which varies with t) and y(t) satisfying the equation is the "output".

The differential operator is not y''+y' but y''+y'+y

marlon
 
thank you very much!
 

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