Timeline for Second order differential equation with non constant coefficient

14 events

when toggle format	what		by	license	comment
Dec 15 at 8:03	vote	accept	trying
Dec 13 at 16:47	answer	added	Fred Hucht		timeline score: 3
Dec 13 at 11:30	comment	added	trying		@FredHucht Do you have any reference for this? Your explanation is a bit vague for me.
Dec 13 at 11:30	comment	added	trying		@GeraldEdgar thanks i understand now.
Dec 13 at 8:04	comment	added	Fred Hucht		@trying Ok, my comment remains correct.
Dec 13 at 6:58	history	edited	trying	CC BY-SA 4.0	added 2 characters in body
Dec 13 at 6:57	comment	added	trying		@FredHucht sorry yes, I fixed the typo.
Dec 12 at 15:31	comment	added	Fred Hucht		@trying Please check your 2nd equation, I think it should read $f(t)$ instead of $\sqrt{f(t)}$. Else, there is a factor $1/2$ missing in the first equation.
Dec 12 at 15:15	history	edited	Daniele Tampieri	CC BY-SA 4.0	Minor Math Jaxing and formatting
Dec 12 at 15:13	comment	added	Fred Hucht		The logarithmic derivative $f'(t)/f(t)$ suggests to consider $f(t)=\exp(a_0+a_1 t+a_2 t^2+a_3 t^3)$, which is solved by the tri-confluent Heun function(`HeunT[]` in Mathematica). Simpler cases (some $a_k=0$) give Hermite polynomials, Bessel functions (see comment by @GeraldEdgar), or simple exponentials.
Dec 12 at 14:33	review	Close votes
yesterday
Dec 12 at 14:29	comment	added	Gerald Edgar		If $f(t) = t^a$, then we get solution with Bessel functions... $$C_1t^{(1-a)/2} J_{(1-a)/2}(kt)+C_2t^{(1-a)/2} Y_{(1-a)/2}(kt)$$
Dec 12 at 13:26	history	edited	trying	CC BY-SA 4.0	added 115 characters in body
Dec 12 at 13:03	history	asked	trying	CC BY-SA 4.0