Is This the Correct Method for Solving Differential Equations on Midterms?

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Discussion Overview

The discussion revolves around the methods for solving differential equations as encountered in a midterm exam. Participants are seeking validation of their approaches and answers, focusing on differentiation and integration techniques.

Discussion Character

  • Homework-related, Technical explanation, Debate/contested

Main Points Raised

  • One participant expresses uncertainty about the correctness of their method or answer regarding a differential equation from a midterm.
  • Another participant questions the understanding of differentiation and the origin of a function f(x) mentioned in the context.
  • A participant suggests that the method of integrating with respect to x is appropriate, proposing a specific formulation involving an arbitrary differentiable function f(x).
  • There is a suggestion that the initial answer may be correct, though this is not universally confirmed.
  • Some participants indicate a lack of confidence in their differentiation skills as they seek to verify their solutions.

Areas of Agreement / Disagreement

The discussion reflects uncertainty and a lack of consensus on the correctness of the methods and answers presented. Multiple viewpoints exist regarding the approach to solving the differential equation.

Contextual Notes

Participants have not fully resolved the assumptions underlying their methods, and there are indications of missing details in the differentiation process and the definitions of functions involved.

lyj0211
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Hi, this question came up in my midterm and I was hoping to know if this is the correct method or answer.
 

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What do your trusty differentiation skills tell you? Where did f(x) come from?
 
SteamKing said:
What do your trusty differentiation skills tell you? Where did f(x) come from?

this is my answer, I am just not sure if it is correct.
 
It's correct, I think.
 
lyj0211 said:
this is my answer, I am just not sure if it is correct.

Does that mean that you don't know how to differentiate the function you've found and check whether it satisfies the original equation?
 
lyj0211 said:
Hi, this question came up in my midterm and I was hoping to know if this is the correct method or answer.

You know you're immediately going to integrate with respect to [itex]x[/itex], so you can conserve symbols by writing "[itex]u_x = \dfrac{(\frac 23 t^3 + t)}{1 + x} + f'(x)[/itex] for an arbitrary differentiable [itex]f(x)[/itex]".
 

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