Timeline for General systems of linear differential equations with variable coefficients
Current License: CC BY-SA 3.0
10 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 6, 2018 at 13:01 | comment | added | Pietro Majer | Also: mathoverflow.net/questions/199158/… | |
| Feb 22, 2014 at 15:10 | comment | added | PLG | Thanks for the link! However it seems to me that Picard and Vessiot's theory answers the question negatively when it comes to elementary means but, as pointed by Bryant below, a solution is exactly expressible if one allows for integration procedures. I just realised that indeed, the solution to any system $A(t)v(t)=\dot{v}(t)$ is exactly expressible in terms of the solutions to a $finite$ number of linear Volterra equations of the 2nd kind. | |
| Feb 21, 2014 at 15:08 | answer | added | username | timeline score: 1 | |
| Feb 21, 2014 at 13:31 | comment | added | Piyush Grover | Relevant:mathoverflow.net/questions/140849/solution-of-linear-ode/… | |
| Feb 21, 2014 at 12:32 | answer | added | Robert Bryant | timeline score: 9 | |
| Feb 21, 2014 at 10:24 | comment | added | PLG | Is this series expansion explicitly known at all orders ? And I don't mean something like the Dyson series, I mean something that actually allows you to obtain an explicit analytical form for order $n$. | |
| Feb 21, 2014 at 7:13 | comment | added | Pietro Majer | You have a series expansion for $M$, and in general I'm afraid this is "the best one can hope for". | |
| Feb 20, 2014 at 22:19 | answer | added | Bazin | timeline score: 3 | |
| Feb 20, 2014 at 21:15 | comment | added | Alex Degtyarev | No hope. Say, any second order linear equation can be converted to a system like yours. But even simplest equations don't have "closed form" solutions. | |
| Feb 20, 2014 at 21:06 | history | asked | PLG | CC BY-SA 3.0 |