Understanding the Role of Constants in First Order Differential Equations

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Homework Help Overview

The discussion revolves around the integration of a first-order differential equation, specifically dy/dx = x(1-x). Participants are examining the role of constants and potential typographical errors in the problem statement.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Participants discuss the integration process and the appearance of constants, questioning the source of 't' in the solutions provided. Some suggest there may be a typo in the problem, proposing that the derivative should be dx/dt instead of dy/dx.

Discussion Status

The conversation is active, with participants providing insights and identifying possible errors in the problem statement. There is no explicit consensus on the correct interpretation, but several lines of reasoning are being explored regarding the integration and the nature of the differential equation.

Contextual Notes

There is a suggestion that the original problem may contain a typo, which could affect the interpretation of the differential equation. Participants are considering the implications of this potential error on their solutions.

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solve dy/dx = x(1-x)

I got y = (x^2)/2 - (x^3)/3 + C

however in the solutions they've gotten:

259y0kp.png


where did t come from?
 
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It came when they integrated dt on the right hand side, 2 steps above where you marked the solution.
 
It looks to me like there is a typo in the problem. y disappeared! I think they meant the derivative to be dx/dt, not dy/dx. Your solution to dy/dx=x(1-x) is correct.
 
Oh nice spot!
 
Dick said:
It looks to me like there is a typo in the problem. y disappeared! I think they meant the derivative to be dx/dt, not dy/dx. Your solution to dy/dx=x(1-x) is correct.

Yeah it definitely looks like the problem was supposed to be dx/dt
 
thanks guys
 

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