Solving dy/dx = y+x: General Equation & Substitution Method

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Homework Help Overview

The discussion revolves around solving the differential equation dy/dx = y + x, focusing on finding the general equation and exploring substitution methods.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants discuss potential substitutions, questioning the effectiveness of separating variables and considering functions like x, y, or x+y. There is also mention of integrating factors as a possible approach.

Discussion Status

The conversation is ongoing, with participants offering various suggestions for substitutions and questioning the original poster's understanding of the problem. There is no explicit consensus on the best approach yet.

Contextual Notes

Some participants inquire about the original poster's familiarity with linear equations and constant coefficient equations, indicating a potential gap in background knowledge relevant to the problem.

thereddevils
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Homework Statement



Find the general equation of differential equation dy/dx=y+x

Homework Equations





The Attempt at a Solution



I don see a way to separate the variables. What substitution should i use?
 
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I only see three possible choices for a function in your equation: x, y, or x+y
 
Office_Shredder said:
I only see three possible choices for a function in your equation: x, y, or x+y

sorry but i don get what u meant
 
thereddevils said:
sorry but i don get what u meant

I think Office_Shredder means you should look at the equation and take a guess at what might be a good substitution. What might work?
 
Failing that, you could try an integrating factor of e^{-x}
 
Office_Shredder said:
I only see three possible choices for a function in your equation: x, y, or x+y

thereddevils said:
sorry but i don get what u meant
You said you were looking for a substitution! It wouldn't do much good to let u= x or u= y, would it? So what if u= x+ y?
 
thereddevils said:

Homework Statement



Find the general equation of differential equation dy/dx=y+x

Homework Equations





The Attempt at a Solution



I don see a way to separate the variables. What substitution should i use?

Substitution?? Have you studied linear equations or constant coefficient equations yet?
 

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