Timeline for Analytically solving this second order ODE
Current License: CC BY-SA 4.0
13 events
| when toggle format | what | by | license | comment | |
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| Apr 2 at 10:28 | vote | accept | Dr. phy | ||
| Apr 2 at 7:04 | answer | added | Ulrich Neumann | timeline score: 2 | |
| Apr 1 at 20:23 | comment | added | Dr. phy |
I'm not an expert in MA. So let me ask can this singularity be eliminated? I mean at the integral of NDSolve is there any command that eliminates singularities? Otherwise, the integral can be made from say t=0.1 and also the IC can be evaluated at x[0.1]. So now is there a solution that could be found over a range of k? @UlrichNeumann
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| Apr 1 at 17:20 | comment | added | Ulrich Neumann | @Dr.phy Numerical solution is possible if you can eliminate the singularity I think | |
| Apr 1 at 16:41 | comment | added | Dr. phy | @march. I try to find approximate or series expansion solutions. | |
| Apr 1 at 16:38 | comment | added | Dr. phy | @UlrichNeumann. Can this equation be solved numerically with that range of $k$ parameter ? | |
| Apr 1 at 15:59 | comment | added | Ulrich Neumann |
@Dr.phy Your ode seems to be singulaer near t==0: {Coefficient[eq, x''[t]] /. t -> 0, Asymptotic[eq /. x''[t] -> 0, t -> 0]} (*{-3, -((4 x[0])/(E^2 t)) + (3 Derivative[1][x][0])/t}*)
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| Apr 1 at 15:18 | comment | added | Dr. phy | @UlrichNeumann. $-5<k<5$. | |
| Apr 1 at 15:15 | comment | added | march | Why do you expect there to be an analytic solution to this equation? Analytic solutions are rare, especially for nonlinear equations like yours. I'd be surprised if there was one here, unless you can find some conserved quantities or something to simplify the differential equation. Of course, that's a math problem rather than a Mathematica one. | |
| Apr 1 at 13:32 | comment | added | Hans Olo | Would the quasi-static/subhorizon approximation work in your case? Getting the full analytical solution might be very difficult, that's why there are the Boltzmann codes out there ;-) | |
| Apr 1 at 11:59 | comment | added | Ulrich Neumann |
What is the parameter range of k ?
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| Apr 1 at 11:37 | history | edited | Dr. phy |
edited tags
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| Apr 1 at 11:31 | history | asked | Dr. phy | CC BY-SA 4.0 |