Trying to get this PDE in terms of 'y'

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Discussion Overview

The discussion revolves around the challenge of expressing a partial differential equation (PDE) in terms of the variable 'y'. Participants explore various methods and approaches to manipulate the equation, while addressing the confusion and difficulties faced by the original poster, Jake. The conversation includes technical reasoning and attempts to clarify the steps involved in solving the PDE.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Homework-related

Main Points Raised

  • Jake expresses confusion about how to manipulate the PDE to isolate 'y', noting discrepancies between his work and textbook answers.
  • Some participants suggest posting Jake's attempted solution to facilitate assistance.
  • One participant proposes that solving the equation is straightforward and asks for clarification on whether Jake wants to express the PDE in a specific form.
  • Another participant introduces the method of separation of variables, suggesting a form y = X(x)T(t) and discusses its implications.
  • Further contributions detail the method of characteristics and transformations involving new variables, but Jake struggles to follow these explanations.
  • Participants mention the need for boundary and initial conditions to solve the PDE, emphasizing that solving it directly may not be feasible without additional information.
  • There is a discussion about the prerequisites for understanding PDEs, with some participants recommending that Jake learn about ordinary differential equations (ODEs) first.
  • Jake expresses a desire to have the equation solved purely in terms of the original variables, questioning the presence of arbitrary constants in the solution.

Areas of Agreement / Disagreement

Participants do not reach a consensus on how to proceed with isolating 'y' in the PDE. There are multiple competing views on the methods to use, and Jake's confusion remains unresolved throughout the discussion.

Contextual Notes

Participants note that understanding ODEs is crucial for tackling PDEs, and some express that the complexity of the problem may exceed Jake's current knowledge level. There are also mentions of the need for boundary and initial conditions, which are not provided in the discussion.

  • #31
Go back to the original equations:
<br /> X&#039;&#039;(x)+\lambda^{2}X(x)=0,\quad T&#039;&#039;(t)+\lambda^{2}T(t)=0<br />
What are the solutions to these equations?
 
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  • #32
An nth order ordinary differential equation always involves n unknown constants. An nth order partial differential equation always involves n unknown functions.

I pretty much told you before that the general solution to that differential equation is
y= F(x- vt)+ G(x+ vt) where F and G are arbitrary, twice differentiable, functions.

The simple fact is that you are trying to do a problem that is far beyond your knowledge. If you do not know how to solve basic ordinary differential equations, no one is going to be able to tell you how to solve partial differential equations in a few sentences.
 
  • #33
I agree with Ivy. Everyone here is trying to help you (the OP) solve the problem, but it's your inexperience that's stopping you from understanding the solution process. PDEs are fairly difficult to solve a lot of the time even for people with a fair amount of math under their belt. I do appreciate your bravado in tackling the wave equation and applaud your desire to extend your mathematical prowess, however I think you should spend a bit more time learning the fundamentals.

It's for a physics paper I'm working on; I don't need to understand all the mathematical concepts, I just need the equation solved for y please.

About this, you can't just expect to post a problem and get a detailed solution back. It doesn't work that way. IMHO, the forums are really an aid to your own problem solving. If you're looking for the other kind of problem solving, try http://www.wolframalpha.com/" .
 
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