# First Order Homogeneous Equation

1. Sep 19, 2009

### mattbonner

1. The problem statement, all variables and given/known data

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

2. Relevant equations
substitute y = xv
dy = dx v + dv x

3. 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?

2. Sep 19, 2009

### HallsofIvy

Staff Emeritus
What reason do you have for thinking you are doing anything wrong?

3. Sep 19, 2009

### mattbonner

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: Sep 19, 2009
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