Partial Differential Equation? What is this?

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Homework Help Overview

The discussion revolves around a homework problem related to partial differential equations, specifically involving a substitution method to find a solution of a given form.

Discussion Character

  • Exploratory, Conceptual clarification, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the nature of the problem and the method of substitution into the differential equation. Questions arise about how to begin the substitution process and what specific forms of functions are required to satisfy the equation.

Discussion Status

Some participants have provided guidance on substituting a specific function form into the differential equation, while others express confusion about the substitution process and seek clarification on the steps involved.

Contextual Notes

There is mention of a specific equation, du/dt = D*(d2u/dx2), which is central to the discussion, but participants are uncertain about how to apply it to their problem.

JefeNorte
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The professor passed this out today for homework and I have no idea how to even get started. If someone could tell me what type of problem this is I could look it up in the textbook but I can't find anything similar. I couldn't figure out how to insert all of the symbols so I attached the problem as a .gif
 

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What exactly is your problem? The paper leads you step by step through the solution. It says

"Seeking a solution of the form u= f(x) cos([itex]\omega[/itex]t)+ g(x) sin([itex]\omega[/itex]t), show that ..."

Okay, put that into the differential equation and see what must be true of f and g in order to satisfy the equation.
 
Last edited by a moderator:
I have been trying to figure out this problem for a week now and I am still drawing a blank on how to "put that into the differential equation." How exactly can I get started on this?
 
Do you know how to "substitute" into an equation? The problem is askng you to substitute u= f(x) cos(t)+ g(x) sin(t) into the equation and tell what must be true of f and g in order to satisfy the equation.
 
I'm not sure I understand exactly what you are talking about. What am I substituting u= f(x) cos(t)+ g(x) sin(t) into? The du/dt=D*(d2u/dx2) equation?
 
Yes! That's the only equation you are given at that point!
 

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