Question

solve the seperable equation:
x(dv/dx)= (1-4v^2)/3v
im not sure how to get to the final answer

Answer 1

I already worked this one out for you...

Answer 2

x(dv/dx)= (1-4v^2)/3v
[3v/(1-4v^2)] dv =dx/x
let u=1-4v^2, du=-8vdv
-(3/8)du/u=dx/x
-3/8 lnu =lnx +c
-3/8 ln(1-4v^2) =lnx +c