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Apr
16
awarded  Necromancer
Apr
12
comment maximal ideal of a polynomial ring
They are ideals, indeed. Just not maximal. Do you see why?
Mar
28
awarded  Nice Question
Mar
15
answered Passing from basis of topology to regular definition of open sets
Mar
10
awarded  Nice Question
Mar
3
accepted How to solve $tx'(t) = (2t^2 + 1)x(t) + t^2$?
Mar
3
comment How to solve $tx'(t) = (2t^2 + 1)x(t) + t^2$?
Yes that's what I meant when saying $c = \sqrt(\pi)/2$. Still am clueless on how to proceed, I must shamefully admit.. Thanks for your help in any case! :)
Feb
26
accepted Find the limit of $x_n = \sin(2\pi (n^3 − n^2 + 1)^{1/3} )$
Feb
26
asked Find the limit of $x_n = \sin(2\pi (n^3 − n^2 + 1)^{1/3} )$
Feb
26
comment How to solve $tx'(t) = (2t^2 + 1)x(t) + t^2$?
with a lot of work I was able to show the limit is bounded from above by 1/2 (or -1/2, I lost track of the sign). Since the function we're taking the limit of is increasing, this shows the limit exists.. But I am using $t \cdot \int_{t}^{t+k} e^{-x^2}dx < \int_{t}^{t+k} t \cdot e^{-x^2}dx $ and I cannot see any other way to do it without this strict inequality.. Could you give another hint on how to proceed?
Feb
26
comment How to solve $tx'(t) = (2t^2 + 1)x(t) + t^2$?
Whoops I meant $-\sqrt(\pi)/2$ of course..
Feb
26
comment How to solve $tx'(t) = (2t^2 + 1)x(t) + t^2$?
Yes I guess $c$ should be $\sqrt(\pi)/2$ if we set $t_0 = 0$. I am trying out different approaches now to calculate this limit, but without success so far..
Feb
26
comment How to solve $tx'(t) = (2t^2 + 1)x(t) + t^2$?
@Amzoti I just learned about the integrating factor, thanks for the reference! Is the thing I stumbled upon what you meant with "something seems wrong"?
Feb
26
revised How to solve $tx'(t) = (2t^2 + 1)x(t) + t^2$?
added 630 characters in body
Feb
26
comment How to solve $tx'(t) = (2t^2 + 1)x(t) + t^2$?
@Amzoti , yes I just rechecked. It is question number 10 from mathematics.ceu.edu/sites/mathematics.ceu.hu/files/attachment/… if you want to take a look.
Feb
26
asked How to solve $tx'(t) = (2t^2 + 1)x(t) + t^2$?
Feb
26
comment Integration of $\int_{-\infty}^{\infty} e^{-x^2 + 2x} dx$
Thanks for the answer Tim. The other addressed my question slightly more directly, so I accepted that one. Nevertheless your one was useful as well!
Feb
26
comment Integration of $\int_{-\infty}^{\infty} e^{-x^2 + 2x} dx$
That is great @kobe, I will check it out.
Feb
26
comment Integration of $\int_{-\infty}^{\infty} e^{-x^2 + 2x} dx$
Hi Kobe, could you state the other ways from the "number of ways"? I'll check them out via google. Thanks!
Feb
26
accepted Integration of $\int_{-\infty}^{\infty} e^{-x^2 + 2x} dx$