Differential equation of dy/dx = (2x-y+4)/ (4x-2y +1)

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Homework Help Overview

The discussion revolves around solving the differential equation dy/dx = (2x-y+4)/(4x-2y+1) using the transformation v = 2x - y. Participants are examining the differences between their results and the provided answer, particularly focusing on the implications of constant summands in the context of solutions to differential equations.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • The original poster attempts to understand the discrepancy between their result and the given answer, specifically questioning the addition of a constant term in the solution. Other participants explore the reasoning behind the constant summand and its relevance to the solutions of differential equations.

Discussion Status

The discussion is ongoing, with participants providing insights into the nature of solutions to differential equations and the role of constants. There is recognition that differing methods may lead to variations in the form of the solution, but no consensus has been reached regarding the necessity of the constant term.

Contextual Notes

Participants are navigating the implications of constant terms in their solutions, with some questioning the author's approach and the assumptions underlying the transformation used. The context of the homework assignment may impose specific requirements that influence the discussion.

hotjohn
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Homework Statement


I'm asked to use the transformation of v= 2x-y to solve dy/dx = (2x-y+4)/ (4x-2y +1) the answer given is (2/9)(6x-3y-2) +(7/9)ln(6x-3y-2) = x +c , i got (2/9)(6x-3y) +(7/9)ln(6x-3y-2) = x +c , what's wrong with my working ?

Homework Equations

The Attempt at a Solution

 

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The two answers differ by a constant summand of 4/9. As you have "+c" anyway, this difference does not matter.
 
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mfb said:
The two answers differ by a constant summand of 4/9. As you have "+c" anyway, this difference does not matter.
lol , why the author want to dd in another (2/9)(-2) into the answer ? this is confusing ...
 
Presumably, because the author used a different method to arrive at a solution. In any case, the point is that, because the derivative of a constant is 0, two functions, differing by a constant, can be solutions to the same first order differential equation.
 
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