How to Solve a Non-Separable Differential Equation?

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Homework Help Overview

The problem involves solving a non-separable differential equation of the form dy/dx = -(4x+4y) / (4x+4y-2), with a substitution v = x + y. The original poster expresses difficulty in separating variables and identifying errors in their working process.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the substitution v = x + y and its implications for the derivative dv/dx. There are questions about the correctness of the original poster's calculations and signs, as well as attempts to clarify the relationship between v, x, and dy/dx.

Discussion Status

The discussion includes attempts to clarify the differentiation process and correct any mistakes in the original poster's approach. Some participants have provided feedback on specific errors, and the original poster indicates they have resolved their issue after receiving guidance.

Contextual Notes

There is mention of an expected answer format, which may influence the approach taken by participants. The original poster's initial confusion about separability and signs suggests a need for careful consideration of the problem's setup.

hotjohn
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Homework Statement


i was given dy/dx = -(4x+4y) / (4x+4y-2) , v= x +y . I have tried to do ( as in the photo) , but I didn't get the ans , in the last line of my working , the V and x are not separable , which part of my working is wrong ?

Homework Equations

The Attempt at a Solution

 

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If v = x+y, then dv/dx = 1 + dy/dx, not x + dy/dx as you wrote.
 
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phyzguy said:
If v = x+y, then dv/dx = 1 + dy/dx, not x + dy/dx as you wrote.
i have redone the question , but i gt stucked here , how to proceed?

btw , the ans given is - ( (x+y) ^2 ) +(x+y ) = x +A
 

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Check your signs again.
 
phyzguy said:
Check your signs again.
ok , i gt it correct now , thanks
 

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