Homework: Finding an antiderivative

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Homework Help Overview

The problem involves finding an antiderivative related to the differential equation dy/dx = y(1-y), which falls under the subject area of differential equations.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants discuss the method of separation of variables and whether the equation can be separated into functions of x and y. There is an exploration of the conditions under which separation is possible.

Discussion Status

The discussion is ongoing, with participants questioning the separability of the equation and clarifying the conditions for applying the separation of variables technique. Some guidance has been offered regarding the nature of the equation.

Contextual Notes

There is a noted absence of an x variable on one side of the equation, which leads to confusion about the ability to separate variables. Participants are encouraged to revisit their notes for clarity.

twinebiscuit
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Homework Statement


dy/dx = y(1-y)


Homework Equations





The Attempt at a Solution


dx = dy(y(1-y))?
 
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What do you know about separation of variables ?
 


that you can separate them if there is an x and a y on the right side of the equation and they are multiplying
 


Alright, so can you separate x and y in your equation ?
 


I don't think so because there is no x on the right side it's only y?
 


Alright, then, you must reread your notes, because the equation you posted is separable, as it's a simpler case of the general

[tex]\frac{dy}{dx} = X(x)Y(y)[/tex]

In your case, X(x)=1, so the variables can be separated.
 

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