1st order, non linear, homogeneous, ODE

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Homework Help Overview

The discussion revolves around solving a first-order, non-linear, homogeneous ordinary differential equation (ODE) given by the expression "3u+(u+x)u'=0". Participants express their challenges in understanding the problem and exploring potential methods for solving it.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the use of v-substitution and express confusion about its application. There are inquiries about what substitutions might be appropriate and whether the method of integration factors could be relevant.

Discussion Status

The discussion is ongoing, with participants sharing their attempts and seeking clarification on their approaches. Some participants are questioning their understanding of v-substitution and exploring different ways to interpret the problem. There is no explicit consensus on a method yet, but the dialogue indicates a collaborative effort to navigate the problem.

Contextual Notes

Participants note that this is their first week's homework and express concern about the pace at which the material was covered in class. There are no specific equations provided for guidance, and the variables x and u are acknowledged as part of the problem context.

Schmoozer
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Homework Statement



"Solve the following ODE's:"
"3u+(u+x)u'=0"

This is our first weeks homework and he went this through this so quickly in class.

Homework Equations



None. x and u are both variables.

The Attempt at a Solution


I know it is homogeneous and non linear. I tried v-substitution and just couldn't get a v to fit. Do i need to use the method of integration factor?

Thanks guys!
 
Last edited:
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Schmoozer said:
I tried v-substitution and just couldn't get a v to fit.
Why doesn't this work? What do you understand by v-substitution?
 
Not much, I feel like I'm guessing... any suggestions what i should substitute?
 
Schmoozer said:

Homework Statement



"Solve the following ODE's:"
"3u+(u+x)u'=0"
Perhaps better to rewrite it as
[tex]u'= \frac{-3u}{u+x}= \frac{-3\frac{u}{x}}{\frac{u}{x}+ 1}[/tex]

This is our first weeks homework and he went this through this so quickly in class.

Homework Equations



None. x and u are both variables.

The Attempt at a Solution


I know it is homogeneous and non linear. I tried v-substitution and just couldn't get a v to fit. Do i need to use the method of integration factor?

Thanks guys!
 
-(1/4)ln|(u/x)|=ln|x|+c ?

Thanks so much. This class is like diffy eq on steroids and wasn't very good at diffy eq.
 

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