01:640:115 Lecture 8: Pre-Calc, Lew Hirsch, section 3.2 Polynomial functions page 3

?S FdS for F(x,y,z)= <-y,z,-x>,G(u,v)=(u+3v,v-2u,2v+5),0?u?1,0?v?1

dy/dx= (x^2-y^2)/(3xy)

The answer is supposed to be (x^2 - 4y^2)^3(x^2 )= C

-----------------------------
Here is what I have done:
x/(3y) - y/(3x) = (1/3)(x/y - y/x) = (1/3)(1/(y/x) - y/x)

v = y/x

dy/dx = v + x dy/dx

xdv/dx = 1/(3v) - 2v/3

dv/dx = (1/x)(1/(3v) - 2v/3)

integral of 3v(1-2v^2)^(-1)dv = lnx + C