D.E. Wronskian Method: Stuck trying to show L.I. and L.D. intervals

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Homework Help Overview

The discussion revolves around the Wronskian method in the context of linear independence and dependence of functions, particularly in relation to differential equations. Participants are attempting to identify intervals where the Wronskian indicates linear independence or dependence.

Discussion Character

  • Exploratory, Assumption checking, Conceptual clarification

Approaches and Questions Raised

  • Participants discuss the conditions under which functions are considered linearly independent or dependent based on the Wronskian. There are inquiries about procedural steps and the meaning of specific terms related to the Wronskian.

Discussion Status

The conversation is ongoing, with some participants expressing confusion about the concepts and seeking clarification. There is a recognition that the Wronskian vanishes at specific points, leading to questions about the implications of this for intervals of linear dependence or independence. Multiple interpretations of the problem are being explored.

Contextual Notes

Some participants question the clarity of the original problem and whether it effectively conveys the intended learning objectives regarding the Wronskian and linear dependence. There is also mention of the potential for misunderstanding the nature of intervals in this context.

  • #61
Jeff12341234 said:
Well we got our tests back. The correct answer for part A was (-inf, 0) but he said any of the three intervals could've been used. It was L.I. on the intervals (-inf, 0) U (0, 2/7) U (2/7, inf). I got part A correct on the test.

Part B was really weird. The answer was "any interval that contained the two points" so (-inf, inf) could've been used. I got this part wrong.

Weird stuff..

I don't think the person that composed the questions and answers really understands that "linearly dependent" is different from "wronskian equals zero". The PlanetMath site seemed to have a similar delusion. Hopefully, you do. Someday you might get a test question from someone who does.
 

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