Solving 2tv' - v = 0: Is it Separable?

[seand]

How do you find a solution for:

2tv' - v = 0

The text says it's separable but I'm not seeing it. I'm just learning so extra details are appreciated. Thanks.

(this should have been posted in the homework section - but I can't seem to move it there, sorry)

 

[Mark44]

2t dv/dt = v
==> 2t dv = v dt
Can you continue?

 

[seand]

well I think I want to switch things around so v and t are separated

1/v dv = 1/2t dt

integrating both sides
ln(v) = 1/2 ln(t)+C

e^x both sides:
v = k*sqrt(t)

Which looks right! Is that how I was meant to do it? If so, thanks - I got stalled before when I got the ln() on both sides.

 

[Mark44]

Looking right might not be good enough. You can check by taking the derivative and verifying that tv' - v = 0.

 

[Unit]

Looking right might not be good enough. You can check by taking the derivative and verifying that tv' - v = 0.

Verifying that 2tv' - v = 0