# Differential equations separation of variables

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

I used seperation of variables to get

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

I'm not sure if thats even right.

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

Integral
Staff Emeritus
Gold Member
Your Separation of variables looks good, now a simple substitution finishes the job.

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

I used seperation of variables to get

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

I'm not sure if thats even right.

But if it is right, how do I integrate that?
You made a slight mistake with the variable seperation--- you can't have dx in the denominator! (Atleast, I've learnt 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. :)