First Order Homogeneous Equation

  • Thread starter mattbonner
  • Start date
  • #1
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Homework Statement



(4y4-9x2y2-144)dx - (5xy3)dy = 0


Homework Equations


substitute y = xv
dy = dx v + dv x


The Attempt at a Solution


after substituting i got

(4x4v4-9v2x4-14x4)dx - (5v3x4)dx.v + dv.x

= (4v4-9v2-14)dx - 5v3(dx.v + dv.x) = 0
= dx(4v4-9v2-14-5v4)+dv(-5v3x)= 0
dx/x = (-5v3dv)/(v4-9v2-14)

dx/x = ((2v)/(v2+2) - (7v)/(v2+7)) dv

derive both sides

ln(x) = ln(v2+2) - 3.5ln(v2+7)
x + c = (v2+2) / (v2+7)3.5

c = (((y/x)2+2) / ((y/x)2+7)3.5) - x


what am i doing wrong?
 

Answers and Replies

  • #2
HallsofIvy
Science Advisor
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What reason do you have for thinking you are doing anything wrong?
 
  • #3
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webworks (the online assignment thing my school uses) is telling me my answer is incorrect

nvm i know where the mistake was made
 
Last edited:

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