Differential equations - new subject help needed

The question is: By separating the variables, find the general solutions of the following differential equations

For this one :-

dv/dt = t((v^2) - 4)

I end up with
v^2 = Ae^(t^2) +4

The book answer is v = 2(1+ A^(2t^2))/(1-Ae^(2t^2))

There is no e in the numerator which is possibly a typo but may be not.

What is the maths that gets from v^2 to v?

Reply 1

ghostwalker

Original post by maggiehodgson

Yes, that's just a typo.

What is the maths that gets from v^2 to v?

More to the point, how did you get v^2 in the first place? It doesn't arise when I did it.

Outline:

Separate variables.
Partial fractions on the v functions.
Integrate.
Combine ln functions.
Exponentiate
Rearrange.

SPICER - woo!

Reply 2

maggiehodgson

Original post by ghostwalker

Yes, that's just a typo.

More to the point, how did you get v^2 in the first place? It doesn't arise when I did it.

Outline:

Separate variables.
Partial fractions on the v functions.
Integrate.
Combine ln functions.
Exponentiate
Rearrange.

SPICER - woo!

How did I get v^2? By being stupid and integrating v^2 - 4 to 0.5ln(v^2 -4). I didn't even have a 2v. Wrong in so many ways.

I have lost all my C4 stuff by not having to use it since June. Oh dear me.

Thank you for the reminder and the acronym.

Thanks again.