Differential equations separation of variables

[EP]

xdv/dx=(1-4v^2)/3v

I used separation of variables to get

x/dx=(1-4v^2)/3v dv

I'm not sure if that's even right.

But if it is right, how do I integrate that?

 

[Integral]

Your Separation of variables looks good, now a simple substitution finishes the job.

 

[Pseudo Statistic]

xdv/dx=(1-4v^2)/3v

I used separation of variables to get

x/dx=(1-4v^2)/3v dv

I'm not sure if that's even right.

But if it is right, how do I integrate that?

You made a slight mistake with the variable separation--- you can't have dx in the denominator! (Atleast, I've learned not to do it)
You should have done:
xdv = (1-4v^2)/3v dx
dx/x = 3v/(1-4v^2) dv
Integration from there is pretty simple... apply your initial conditions. :)