Please check my work: verify that the equation is homogeneous

[darryw]

Homework Statement

verify the equation is homogeneous and solve.. thanks

(x^2 - 2y^2)dx + (xy)dy = 0

(x^2 - 2y^2) = -(xy)dy/dx

(x^2 - 2y^2)/-(xy) = dy/dx

-(x/y) - 2(y/x) = dy/dx



v = (y/x) .. y = vx and dy/dx = v + xv'




-(1/v) - 2v = v + xv'

x(dv/dx) + (1/v) + 3v = 0

3v + (1/v) = -x(dv/dx)

(3v + (1/v))/dv = -x/dx

(1/3v + v)dv = (1/x) dx

1/9v^3 + 1/2v^2 = ln|x| + c

Homework Equations

The Attempt at a Solution

 

[Nino MMP]

The equation is homogeneous since it is a function of x and y with no constants. The solution is: 1/9v^3 + 1/2v^2 = ln|x| + c