How to Solve This ODE Using Mathematica?

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SUMMARY

The forum discussion centers around solving the ordinary differential equation (ODE) given by (7x^3+3x^2y+4y)dx+(4x^3+x+5y)dy=0 using Mathematica or MuPAD. The equation is expressed in the form M dx + N dy=0, where M=7x^3+3x^2y+4y and N=4x^3+x+5y. The user has attempted the integration factor technique without success and is seeking assistance in finding a solution. The discussion highlights the potential use of integral transforms if initial conditions are provided.

PREREQUISITES
  • Understanding of ordinary differential equations (ODEs)
  • Familiarity with Mathematica 12.0 or MuPAD for symbolic computation
  • Knowledge of integration factors in differential equations
  • Basic concepts of integral transforms
NEXT STEPS
  • Research how to apply integration factors to non-exact ODEs
  • Learn how to use Mathematica for solving differential equations
  • Explore the method of integral transforms for ODEs
  • Study examples of solving ODEs using MuPAD
USEFUL FOR

This discussion is beneficial for students and professionals in mathematics, particularly those studying differential equations, as well as users of Mathematica or MuPAD seeking to enhance their problem-solving skills in this area.

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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