Differential equations y''-xy'+2y=0?

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Discussion Overview

The discussion revolves around solving the differential equation y'' - xy' + 2y = 0. Participants explore methods for finding solutions, particularly focusing on power series and the application of different types of series expansions.

Discussion Character

  • Homework-related
  • Mathematical reasoning
  • Debate/contested

Main Points Raised

  • One participant expresses confusion about solving the differential equation and requests help, indicating a lack of support from their teacher.
  • Another participant suggests that the equation is a linear homogeneous differential equation with variable coefficients and recommends using power series to find a solution.
  • A different participant questions the use of two types of series expansions, asking when to use each type and how to apply them in the context of another differential equation.
  • One participant admonishes another for posting the same question in multiple threads, indicating a concern for discussion etiquette rather than addressing the mathematical content.

Areas of Agreement / Disagreement

The discussion contains multiple competing views regarding the methods for solving the differential equation, with no consensus reached on the best approach or the specifics of applying different series types.

Contextual Notes

Participants express uncertainty about the application of power series and the specifics of the recurrence relations involved in solving the differential equation. There are also unresolved questions about the conditions under which different series expansions should be used.

hawaiidude
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how would you solve

y''-xy'+2y=0?

it says, {2a2+6a3x+12a4x^2+...n(n-1_anx^n-1

ahh i don't know..how would you solve this? can someone explain? my math teacher is un willing to help me...
 
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You mean your teacher is unwilling to tell you the answer. How mean of him! Does he expect you to actually LEARN how to do it?

The problem you have is a linear homogeneous d.e. with variable coefficients. The standard way of solving such an equation is to use power series (as you can see from the given solution).

Let y= Σ anxn where the an are to be determined. Calculate the derivatives of that, plug into your equation and combine like powers of x. You will get a recurrence relation for the ans.
 
yeah..thnaks but why are there two types of reserection and when do i use them? like sigma n=0 anX^n and other one with the & lambda ; x^ sigma anX^n...when do i use which ones and how? and how do i plug in answers in the differential equation/ like 8x^2y''+10xy'+(x-1)y=0
x^ &lambda ; {8 &lambda ; -1) a0 +10 &lambda ; ...and so on...any help is welcomed
 
Please do not post the same thing on different threads. I responded to this on a different thread.
 

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