D.E.: Reduction of Order: Non-shortcut method question

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Homework Help Overview

The discussion revolves around a differential equation problem involving the reduction of order method, specifically addressing the manipulation of terms like x^3*e^x in the context of solving for a function u(x).

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • The original poster expresses confusion about handling the term x^3*e^x and its implications for solving the equation. There is a question about whether to ignore factors not containing the u(x) function, indicating a need for clarification on this approach.

Discussion Status

Some participants have provided affirmations regarding the correctness of an answer, but there remains uncertainty about the methodology, particularly concerning the treatment of certain terms in the equation.

Contextual Notes

There is a mention of an example provided by the instructor that may not directly apply to the current problem, suggesting potential differences in problem setup or assumptions that need to be considered.

Jeff12341234
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I don't know what to do with the x^3*e^x on the left side of the page. In the example the instructor gave for a different problem, you couldn't solve for x. In this problem you can so what does that mean I need to do with it?

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Is this answer correct?
 
Yes, it is :)
 
So do you always just ignore the factor that doesn't contain the u(x) function like I just did in this example?
 

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