I Solving a nonlinear first order differential equation

Chromatic_Universe

Gold Member
13
0
(a'[t]/a[t])^2 == K*(A + B*a[t]^-6)^1/2} is the equation to be solved for getting the solution of a(t) in terms of time(t). Any ideas on how to solve this problem? Use of Matlab or Mathematica is accepted.
 

Orodruin

Staff Emeritus
Science Advisor
Homework Helper
Insights Author
Gold Member
2018 Award
15,850
5,847
Are you after an analytic or a numerical solution? The numerical solution should be rather straight-forward in both Matlab and Mathematica. Just insert the differential equation along with your initial conditions into the appropriate differential equation solver.
 

Chromatic_Universe

Gold Member
13
0
Are you after an analytic or a numerical solution? The numerical solution should be rather straight-forward in both Matlab and Mathematica. Just insert the differential equation along with your initial conditions into the appropriate differential equation solver.
I am looking for an analytical solution. Sorry for missing that out.
 

Orodruin

Staff Emeritus
Science Advisor
Homework Helper
Insights Author
Gold Member
2018 Award
15,850
5,847
Your differential equation is separable. You could just solve for ##dt## in terms of ##da## and ##a## and integrate. However, doing so will likely result in a hypergeometric function.
 

Chromatic_Universe

Gold Member
13
0
Your differential equation is separable. You could just solve for ##dt## in terms of ##da## and ##a## and integrate. However, doing so will likely result in a hypergeometric function.
I do get a Hypergeometric solution while solving in Mathematica, but is there any physical implication of this solution?
 

phyzguy

Science Advisor
4,247
1,222
I do get a Hypergeometric solution while solving in Mathematica, but is there any physical implication of this solution?
Since we don't know what a(t) represents, how could we know the physical implications?
 

Chromatic_Universe

Gold Member
13
0

Orodruin

Staff Emeritus
Science Advisor
Homework Helper
Insights Author
Gold Member
2018 Award
15,850
5,847
Well, yes, the scale factor’s behaviour with time gives you some physical information. It is usually easier to consider the behaviour of the derivatives if you want to know how your spacetime behaves.
 

Chromatic_Universe

Gold Member
13
0
Well, yes, the scale factor’s behaviour with time gives you some physical information. It is usually easier to consider the behaviour of the derivatives if you want to know how your spacetime behaves.
I was thinking what is physically implicated by the hypergeometric behaviour of the a(t).
 

Want to reply to this thread?

"Solving a nonlinear first order differential equation" You must log in or register to reply here.

Related Threads for: Solving a nonlinear first order differential equation

Replies
11
Views
19K
Replies
1
Views
1K
Replies
8
Views
1K
Replies
6
Views
2K
Replies
2
Views
1K
Replies
22
Views
37K

Physics Forums Values

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving

Hot Threads

Top