Differential equations - new subject help needed Watch

maggiehodgson
Badges: 14
Rep:
?
#1
Report Thread starter 4 years ago
#1
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?
0
reply
ghostwalker
  • Study Helper
Badges: 16
#2
Report 4 years ago
#2
(Original post by maggiehodgson)
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.
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
maggiehodgson
Badges: 14
Rep:
?
#3
Report Thread starter 4 years ago
#3
(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.
0
reply
X

Quick Reply

Attached files
Write a reply...
Reply
new posts
Latest
My Feed

See more of what you like on
The Student Room

You can personalise what you see on TSR. Tell us a little about yourself to get started.

Personalise

University open days

  • Cranfield University
    Cranfield Forensic MSc Programme Open Day Postgraduate
    Thu, 25 Apr '19
  • University of the Arts London
    Open day: MA Footwear and MA Fashion Artefact Postgraduate
    Thu, 25 Apr '19
  • Cardiff Metropolitan University
    Undergraduate Open Day - Llandaff Campus Undergraduate
    Sat, 27 Apr '19

Have you registered to vote?

Yes! (125)
39.06%
No - but I will (17)
5.31%
No - I don't want to (20)
6.25%
No - I can't vote (<18, not in UK, etc) (158)
49.38%

Watched Threads

View All