Thanks to all of you and the last question then you get

dsolve({ode,St(0)=1},St(t),series); 

How should I expand series to n=10. I mean then you have 

                        11   2     11    3      143     4
  St(t) = 1 - 1/12 t + ---- t  - ------ t  + --------- t  +
                       3456      165888      286654464

            2629      5      6
        ------------ t  + O(t )
        206391214080


I want 10 numbers instead of 5. And how do I convert this to polynom.

Moderators note: edited for re-formatting.
@lomkes: set your input format to 'filtered HTML', then you see what you have typed in
 

forgot to mention I need the series with t, which I could on paper to put any t in series and get an answer with (0,12345) accuracy or (0,12345678) accuracy.

one set is km=11, S0=1, v=1 and I need 5numbers acurracy like (0,12345) 5numbers after comma since S0 goes to 0 and then reaction stops.

other km=0.1; v=0.22; S0=0.2; 0.5; 1.0; 1.15; 2.0; 3.0. For 0.2 and 0.5 (0,123456789) and 1.0, 1.15, 2.0, 3.0 I need (0,12345).

S[t] can't be greater than S0 since if t=0, S[t]=S0. t is only positive since it's time.

Yes. it was requested to express this function in series and it was said it's the point. If I wasn't instructed to do series I wouldn't even bother cause it's easy way. You get the S[t] function and count it with maple, but the point is to get series and as I saw it's kinda hard way.

I want numbers instead of that lumbertW thing. And I need to express that thing in series there t=0..x(x-any non negative number). If lumbert series is

                      infinity
                        -----       (n - 1)  n
                         \      (-n)        x
                          )     --------------
                         /            n!
                        -----
                        n = 1

and I got

                                      -v t + S0
                               S0 exp(---------)
                                         Km
                 s := LambertW(-----------------) Km
                                      Km

how do I put 2nd eq to first maybe. to get rid of that lumbertw thing and get only numbers?? Or is
there any other series I can use. The thing is I get one answer of s: and different then I express
it in series. Shouldn't they be the same?

Any chance to get rid of that LambertW in other way. I mean first get values instead of LambertW and then expand the thing with series (taylor or smth else)?? If so then how??

Yeah I wanted values instead of LambertW(as from help I didn't really know what it is), also I needed to get answer in series too (Taylor series came first in my mind since as you see I am not really great in math). And the last question then I try to plot plot(s, t=0..5); I get this Error, (in plot) expected a range but received t = 0 .. 5. Any chance to plot in from 0 to t since t=time and it can't be negative.
 

I got S_t function and want to express it in row(ex. taylor maybe) how do I do it??

I mean 0.1, but still get problems. And I solved it but still get problems. If I use different intervals I get different plots :(. I mean on different intervals there are different lowest points on graph, but then I do it by hand I get everything right. I need to plot

S=S₀*(1-v₀/S₀)^t

then

S(0)=S₀

and

v₀=(k₂*E₀*S₀*k₁)/(S₀*k₁+k_-1+k₂)

E₀=0,1; S₀=1; k₁=1; k_-1=1; k₂=10;

How do I plot this t=0.. 30;

Is everything correct for use of any initial parameters?

Thank you for the reply. Everything works fine till last plot line. Then I write it and press enter it says "Error, (in plots/odeplot) input is not a valid dsolve/numeric solution". I am using maple 11 what can be wrong?? And Second thing is how you make second y(t) axis to display E(t) and ES(t). S(t) and E(t) is as they supose to be. but the plot should be like http://terpconnect.umd.edu/~nsw/ench250/michael0.gif (it's mathcad plot). What I need to change to get such plot?? And what's about S(t) my tutor says it can be solved in maple, I just need to think an algorithm, but I don't understand how :(((