Question

at http://tutorial.math.lamar.edu/Classes/DE/Separable.aspx in last example it is not possible to find an explicit solution for this problem, why? And how we can find the intervals of validity from implicit solution? can someone please show me the intervals of validity for this last example?

Answer 1

looks like they did a fancy separable form

Answer 2

im wondering if it could be complexified to obtain a suitable result ... but quite frankly, i do not know

Answer 3

generally speaking, i believe intervals if validity are culled from the process; and at every point that makes something go awry they flag it; like that cos(y) in the denominator to begin with is a redflag

nothing else in the process looks like it goes bad

Answer 4

frankly this is where my knowledge fails as well
I suggest you take OCW's DE class if you wish to delve into things like that.
(I have not yet done so myself, meet you there!)

All I know is that you can't just solve it explicitly, and finding the interval of validity it probably either impossible, or a real pain in the butt.

Answer 5

@TuringTest what is OCW?

Answer 6

Open course ware from MIT
http://ocw.mit.edu/index.htm
the math sections are under science for some reason
I suggest you take the "scholar" version of each class when possible.

Answer 7

ahaaan, what is the scholar version? (is it free?)

Answer 8

yes it's very free :D
for example here is the physics list of classes
http://ocw.mit.edu/courses/physics/
notice the 5th class on the list has Sc in a red box, which means it is the scholar program.
each red box tells you what that version has
there is a scholar for phys1,2, and I think 3
and for Calc1,2,Linear algebra, and DE's

Answer 9

here is the beginning of that Scholar program in mechanics
you can see it takes you step-by-step

Answer 10

http://ocw.mit.edu/courses/physics/8-01sc-physics-i-classical-mechanics-fall-2010/