Solving Non-Exact Equations (2x-4y+6)dx+(x+y-3)dy=0

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Homework Help Overview

The discussion revolves around solving a non-exact differential equation of the form (2x-4y+6)dx+(x+y-3)dy=0, focusing on the challenges of finding an integrating factor or making the equation exact.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • The original poster expresses difficulty in finding an integrating factor, noting that the expressions (P_y-Q_x)/P and (P_y-Q_x)/Q do not yield functions of a single variable. Other participants suggest a substitution method, specifically y=Vx, and inquire about the differentiation of this substitution.

Discussion Status

The conversation is active, with participants exploring different substitution methods and questioning the prerequisites of calculus knowledge. Guidance has been offered regarding the differentiation of the substitution, but no consensus or resolution has been reached yet.

Contextual Notes

There is an implicit assumption that participants have a background in calculus, as indicated by the reference to the product rule for differentiation.

nhrock3
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(2x-4y+6)dx+(x+y-3)dy=0
i can't make integration cofficient
because

(P_y-Q_x)/P is not a function of x and so is the other one

??

for both (P_y-Q_x)/P and (P_y-Q_x)/Q i don't get a function of one variablr i can't make it exact

how to solve it
 
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Try a substitution of y=Vx
 
if i substite by y=vx
what is dy
?
 
Are we allowed to assume that you have taken calculus?
Use the product rule to differentiate y= vx
 

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