Re: question [using result of DSolve]
- To: mathgroup at smc.vnet.net
- Subject: [mg15672] Re: question [using result of DSolve]
- From: Murray Eisenberg <murray at math.umass.edu>
- Date: Sat, 30 Jan 1999 04:29:04 -0500 (EST)
- Organization: Mathematics & Statistics, Univ. of Mass./Amherst
- References: <78pa6k$cn1@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
One way is as follows (note that I'm showing output in a linearlized
form and not in Mathematica Standard form):
In[1]:= soln = First @ DSolve[{P'[t]==0.031P[t], P[0]==5.3}, P[t],t]
Out[1]= {P[t] ->
5.3000000000000 2.718281828459045^0.0310000000000000 t}
In[2]:= P[t_] := Evaluate[P[t] /. soln]
In[3]:= P[100]
Out[3]= 117.64914179164
At this point you can do pretty much anything with the solution
function, e.g.:
In[4]:= Plot[P[t], {t, 0, 100}]
Instead of the original DSolve expression, one might want to get an
exact solution by entering exact numbers as coefficients of the ODE:
In[5]:= Clear[P] (* needed only if P already defined *)
In[6]:= soln = First @ DSolve[{P'[t]==(31/1000) P[t], P[0]==(53/10)},
P[t],t]
Out[6]= {P[t] -> (53/10) E^((31 t)/1000)}
In[7]:= P[t_] := Evaluate[P[t] /. soln]
In[8]:= P[100]
Out[8]= ((53 E^(31/10))/10
In[9]:= P[100.] (* or N[ P[100] ] *)
Out[9]= 117.649
Alice M. Dean wrote:
>
> Hi, I was given this address by a colleague, who said you could quickly
> answer what I think is a very simple question. After I evaluate the
> following in mathematica,
>
> DSolve[{P'[t]==0.031P[t], P[0]==5.3}, P[t],t]
>
> I get a result which is essentially: {{P[t] -> 5.3 E ^(0.031t)}}
>
> inside two sets of curly brackets.
>
> I would now like to compute P[10], P[100], etc. Is there a reasonable
> way to do this? Thanks, Alice Dean
>
> ~~~~~~~~~~~~~~~~~~~~~~~~~
> Alice Dean
> Mathematics & Computer Science Department Skidmore College
> Saratoga Springs, NY 12866
>
> Phone: (518) 580-5286
> Fax: (518) 580-5936
> Skidmore College Information: (518) 580-5000 E-mail:
> adean at skidmore.edu
> WWW: http://www.skidmore.edu/~adean
> ~~~~~~~~~~~~~~~~~~~~~~~~~
--
Murray Eisenberg murray at math.umass.edu Mathematics &
Statistics Dept. phone 413 549-1020 (H) Univ. of Massachusetts
413 545-2859 (W) Amherst, MA 01003-4515