Implicit Differential Equation: dy/dx = xy - y^2

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Discussion Overview

The discussion revolves around the implicit differential equation dy/dx = xy - y^2, specifically exploring how to approach solving it given the initial condition y(1) = 3. The scope includes mathematical reasoning and potential methods for solving differential equations.

Discussion Character

  • Mathematical reasoning
  • Homework-related
  • Technical explanation

Main Points Raised

  • One participant poses the question of finding y(2) given the differential equation and initial condition.
  • Another participant suggests rewriting the equation as dy/dx = y(x - y) and questions if this reformulation aids in understanding.
  • A different participant proposes a straightforward approach of plugging in values to find a solution.
  • There is a warning about potential issues with overloading a circuit, though the context of this warning is unclear and may not directly relate to the differential equation.
  • One participant repeats the suggestion to rewrite the equation, indicating some confusion about the intent behind the original question.

Areas of Agreement / Disagreement

The discussion does not reach a consensus on how to approach solving the differential equation, with multiple suggestions and methods proposed without clear agreement on the best approach.

Contextual Notes

The discussion lacks clarity on the assumptions behind the proposed methods and does not resolve the mathematical steps necessary to find y(2).

European Sens
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If dy/dx = xy - y^2 and y(1) = 3, then y(2) is ?
 
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Hi European Sens! :smile:

Write it dy/dx = y(x - y).

Does that help? :smile:
 
Can't you just start plugging stuff in?
 
danger!

:frown: … not if it might overload the circuit! …:frown:​
 
tiny-tim said:
Hi European Sens! :smile:

Write it dy/dx = y(x - y).

Does that help? :smile:

:confused: are you trying to show him how to sole this DE?
 

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