Solving Separable Differential Equation: dy/dx = (6x^2)/((1+x^3)y)

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Homework Help Overview

The discussion revolves around solving a separable differential equation of the form dy/dx = (6x^2)/((1+x^3)y). Participants are exploring the integration process and the implications of their results.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants are attempting to integrate the equation and discuss the results, questioning the correctness of coefficients and the implications of the square root in the solution. There is also a suggestion to express the equation in different forms.

Discussion Status

The discussion is active, with participants providing feedback on each other's calculations and expressing uncertainty about specific values. There is no clear consensus on the correct coefficient, but multiple interpretations are being explored.

Contextual Notes

Participants mention potential initial conditions and express concerns about integration accuracy, indicating a focus on the details of the solution process.

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Homework Statement


dy/dx = (6x^2)/((1+x^3)y)


Homework Equations





The Attempt at a Solution



it's a separable func. so after integrating, it looks like this (base on my calculation)

y^2 = 36ln(1+x^3)

so how do i find y? is it just sqrt(36ln(1+x^3))

thanks
 
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36? Really? Could you check that again? Aside from that, sure, except y^2=A has two solutions. y=+sqrt(A) and y=-sqrt(A).
 
Dick said:
36? Really? Could you check that again? Aside from that, sure, except y^2=A has two solutions. y=+sqrt(A) and y=-sqrt(A).

is the 36 supposed to be a 4?

brain fart... suddenly forgot how to do integration..
 
Well, I got 4. Doesn't mean it's correct. If you're not sure you'd better check again.
 
I think it's 4 but also I think it's not going to matter too much when you get to the end. :wink:
 
Thanks guys!

i'm pretty sure (lol) it's 4
 
I suggest you also try writing it in the form x=
and also express both forms in terms of an initial condition e.g. xy=0 and/or yx=0.
 

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