Having a hard time understanding whats asked.

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Discussion Overview

The discussion revolves around understanding a problem from an introductory ordinary differential equations (ODE) class, specifically regarding the implicit solution of a differential equation. Participants express confusion over the clarity of the problem statement and the appropriate method to demonstrate the solution.

Discussion Character

  • Homework-related
  • Debate/contested
  • Technical explanation

Main Points Raised

  • One participant expresses difficulty with the textbook's style, finding it overly verbose and lacking clarity, which complicates homework assignments.
  • The participant questions whether to use implicit differentiation or integration to show the implicit solution of the given differential equation.
  • Another participant suggests using LaTeX for clearer communication of mathematical expressions.
  • A third participant argues that the problem's instructions are straightforward and suggests substituting the given solution into the differential equation to verify it, rather than solving the equation from scratch.

Areas of Agreement / Disagreement

There is no consensus on the clarity of the problem statement or the best approach to demonstrate the solution. Participants have differing views on the necessity of additional directions and the method to use.

Contextual Notes

Participants have not reached an agreement on the interpretation of the problem or the methods to apply, indicating a lack of clarity in the textbook's presentation and the problem's requirements.

MidgetDwarf
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Taking an intro ODE class. Class just started and we are using a book, that to me, feels like en encrypted alien language. It is hard to read, but to much words and images, not enough layout. I'm more into theorem/proof style books. The book is too chatty. Well anyways.

It is giving problems trying to do my homework sets. For example.

Show that the implicit solution of 2x sin2 ydxx2 + 10 cos ydy = 0 is given by ln x2 + 10+csc y = c:

This is not explained clearly in the book. ( the directions).

Does this mean to just take the implicit derivative of ln x2 + 10+csc y = c and put into the form that contains the DE.

or does this mean to integrate 2x sin2 ydxx2 + 10 cos ydy = 0.

I am leaning on the implicit differentiation.I already worked out both ways. I am definitely going to get the library and get a book.
 
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You should write it using tex. It is hard to read the equations like this.
 
Yes, please us LaTeX. Your post is close to unreadable.
This should be explained in any good ODE book like Ross.
 
"Show that the implicit solution of 2x sin2 ydxx2 + 10 cos ydy = 0 is given by ln x2 + 10+csc y = c"

I don't know why you would need "directions". It's pretty straightforward English. You could show that by solving the equation and seeing that the given solution is of the type you got but the simpler way is to put that function into the equation and see that the equation is satisfied.

If you were asked to show that x= 2 is a root of [itex]x^3- 6x^2+ 11x- 6= 0[/itex], you could[/b try to solve the equation but it would make more sense to use the fact that you are already given x= 2, substitute that into the equation, and see what you get!
 

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