Question

Hey quick question about Abel's formula

Answer 1

@ganeshie8

Answer 2

So Abel's formula is \[\huge w(y_1,y_2) = ce^{-\int\limits p(t)dt}\] so for higher orders would it be the same haha? I have the question \[ty'''+2y''-y'+ty=0\] then to apply this formula \[y'''+\frac{ 2 }{ t }y''-\frac{ y' }{ t }+y=0\] so I'm guessing p(t) here then is 2/t and then we have \[\huge w(y_1,y_2,y_3)(t) = ce^{- \int\limits p(t) dt}\] then \[\huge w(y_1,y_2,y_3) = e^{- \int\limits 2/t dt}\] then we get \[w(...)(t) = c/t^2\]

Answer 3

Oh ok I just read it on a site here http://ltcconline.net/greenl/courses/204/appsHigherOrder/HigherOrder.htm I guess it does make sense xD

Answer 4

So this theorem is pretty fascinating then wow, saves tons of time to

Answer 5

It seems though it only works for homogenous equations ah

Answer 6

Talking to myself and figuring things out yippe xD

Answer 7

hahah

Answer 8

@Astrophysics Are you college student?.

Answer 9

I guess so!

Answer 10

ah okay. Your question is completely new to me. Thanks for sharing.

Answer 11

Haha yw, this is from higher level maths called differential equations :)

Answer 12

Which is why most of the time I'm asking myself...what does this mean?!

Answer 13

oh you don't have one to get help here:D

Answer 14

is that right? That's why you ask yourself here?:D

Answer 15

Ha, well I asked because I wasn't sure xD and I find it encouraging when I'm on here otherwise I'd probably be doing something discouraging, I'm not a great mathematician but on here when I ask for help from people like ganeshie it makes me happy and makes me want to work harder to understand!
Even if I'm talking to myself like I was earlier it maybe helpful to others haha, and they can join the conversation and add to it!

Answer 16

nice

Answer 17

Lol, yeah OS makes me much more curious about things, I like that :)

Answer 18

Even if I may sound stupid 90% of the time, long as I'm learning who cares xD

Answer 19

Nice, the theory of solutions to second order differential equations extend smoothly to higher order differential eqns!