Homogenous Differential Equation Solution

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Homework Help Overview

The discussion revolves around solving a homogeneous differential equation of the form dy/dx = x + y. Participants are exploring various methods, including substitution and integrating factors, to approach the problem.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the substitution v = x + y and its implications for simplifying the equation. There are questions about the relationship between the integrating factor method and the substitution approach. Some express confusion about the steps involved in the substitution and integration process.

Discussion Status

There is ongoing exploration of different methods to solve the equation, with participants providing insights and questioning each other's reasoning. Some guidance has been offered regarding the use of integrating factors and the nature of the differential equation, but no consensus has been reached on a specific solution approach.

Contextual Notes

Participants note that the original poster's textbook may not cover certain techniques thoroughly, leading to confusion. There is also mention of an initial condition that may affect the solution, but it remains unclear how it integrates into the overall problem-solving process.

  • #31
Orodruin said:
I think that the approach itself is not very different from the variable substitution that you started with (just writing ##v = y + x + 1## rather than ##v = y+x## - you could also see it as making yet another substitution from ##v' = v + 1## to ##u = v+1##, which also gives ##u' = u##). Regardless, only a very ignorant teacher would deduct points for you using a working method unless explicitly asking for something to be solved with a particular method. But of course this is completely up to you.
thats true...to my knowledge the test doesn't explicitly ask for a certain method so thanks for help :)
 
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  • #32
_N3WTON_ said:
Thank you...your insight has been very helpful to me :)
You are welcome:)

ehild
 

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