First Order Homogeneous Equation

[mattbonner]

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?

 

[HallsofIvy]

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

 

[mattbonner]

webworks (the online assignment thing my school uses) is telling me my answer is incorrect

nvm i know where the mistake was made