Question

Why can't some differential equations be solved? Either analytically or even numerically?

Answer 1

becasue we do not have a means whereby we can solve all of them

numerically gets you a good approximation at least

Answer 2

Can all differential equations be solved numerically?

Answer 3

i believe that they can be approximated to any degree of accuracy short of 100%

Answer 4

What are the problems that prevent analytical solutions from being developed? Is this a question of analysis, topology, other??? The system under evaluation is not continuous, or compact or something??? I don't mean to be vague. I'm just confused by DE's and how they are used.

Answer 5

im no expert to ODEs meself; but I do know that they involve integrating functions.

And there are relatively few functions that we are able to "undo" becasue they fit a form that we recognize as a derivative.

Answer 6

those forms that we do not recognize as a derivative cannot be exacted out

Answer 7

e^(-x^2) for one

Answer 8

sin(x^2) is another

Answer 9

also, not all functions can be expressed as an equation

Answer 10

but then, they wouldnt be DE would they :)

Answer 11

Thank you. I remember seeing that some functions cannot be integrated. I've seen your examples before. I guess my question is then what is it about functions that cannot be integrated that makes them unintegrable(?)? I've read a little about Lebesque integration and that some functions that cannot be Riemann integrated can be integrated by the Lebesque integral? Can you provide some intuition on this?

Answer 12

i believe those are integral transforms; and i aint to versed in those yet

Answer 13

Thanks for your help. :)

Answer 14

youre welcome, and good luck with it :)

Answer 15

I have an intuition that math is beautiful and has powerful application. But learning it can be ferociously difficult.

Answer 16

http://www.math.cornell.edu/~bterrell/dn.pdf.......hope this helps!!!

Answer 17

Thanks. I'll check it out.