How to Solve This ODE Using Mathematica?

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Homework Help Overview

The discussion revolves around solving a specific ordinary differential equation (ODE) given in the form of M dx + N dy = 0, where M and N are polynomial expressions in terms of x and y. Participants are exploring methods to solve the ODE, particularly focusing on the integration factor technique and the use of Mathematica or MuPAD for computation.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Participants discuss the difficulty in finding an integration factor and question whether the equation can be made exact. There is also a mention of the possibility of using an integral transform depending on the context of the problem.

Discussion Status

The discussion is ongoing, with participants expressing their struggles and sharing their attempts to find a solution. Some guidance has been offered regarding the potential use of integral transforms, but there is no consensus on the approach to take or the existence of a solution.

Contextual Notes

One participant notes that the problem has been a source of frustration for an extended period, indicating a lack of initial conditions and the challenge of finding an integration factor, which is said to exist according to the problem statement.

hhegab
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Hi,
I have the following ODE, which I could not solve,
(7x^3+3x^2y+4y)dx+(4x^3+x+5y)dy=0.
I have tried to use the integration factor technique, but I could not find one.
It can be put in the form:
M dx +N dy=0, where M=7x^3+3x^2y+4y, and N=4x^3+x+5y.
Can you help me? And How can it be done on mathematica? (or MuPAD)

hhegab
 
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I don't see any way to make this equation exact either. Were you given any initial conditions, or are you to find a general solution? The reason I ask is that, if you were, we may be able to use an integral transform.

Sorry, but I don't know how to use Mathematica.
 
Dear Tom,
This problem appears in my book! I have struggled with it for 2 months (and I shouldn't have done).
Well, I guess I will stop now.
PS.
It is said that it has an integration factor ! I have done my best to find it, but it was not there.

hhegab
 
2 months?! Egad!

I will wrestle with this some more over the weekend. Take a break! :wink:
 

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