Question

solve the seperable equation:

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

Answer 1

v=0, i√6/2,-i√6/2

Answer 2

v=0,
x(dv/dx) = 1/0
!

Answer 3

thank you! i just dont know how you reached that answer

Answer 4

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 +lnc1
-3/8 ln(1-4v^2) =lnx +lnc1
ln(1-4v^2)^(-3/8) =lnx +lnc1
(1-4v^2)^(-3/8) =xc1
1/[(1-4v^2)^(3/8)] =xc1 or
1/c1 = x(1-4v^2)^(3/8)
C= x(1-4v^2)^(3/8)