how to make maxima create equation like i give in attachment

Macrakis,

Here example that I used 'desolve' for my problem,
--------------------------------------------------------------------
eq1:diff(f(s),s)=-sqrt(2)*g(s)*k;

eq2:diff(g(s),s)=k*(sqrt(2)*f(s)-2*h(s));

eq3:diff(h(s),s)=2*k*g(s);

atvalue(f(s),s=0,f0);

atvalue(g(s),s=0,0);

atvalue(h(s),s=0,0);

desolve([eq1,eq2,eq3],[f(s),g(s),h(s)]);

nonzero;
---------------------------------------------------

I manually replace f[4,1] to f(s), f[4,2] to g(s) and f[4,3] to h(s) because
'atvalue' can't accept f[4,1](s), it will give error.

so how to make maxima automatically convert all those f[n,k] function into
f(s),g(s),h(s).....n(s) in code below so that I can used code above to solve
my problem?

--------------------------------------
depends(f,s);
df[n,k] :=
  if n=0
    then 0
  else

diff(f[2*n,k],s)=x*((k-1)*sqrt(n-k+2)*f[2*n,k-1]-k*sqrt(n-k+1)*f[2*n,k+1]);
eqs:makelist(df[2,k],k,1,3);
-----------------------------------------

or maybe there some way that we didn't need to replace the function but make
maxima solve it automatically?

On Thu, Jan 13, 2011 at 12:41 PM, Stavros Macrakis <macrakis at alum.mit.edu>wrote:

> Razif,
>
> In Maxima, you do not assign values to derivatives etc.  You write
> equations and can store the equations in variables or lists.
>
> Let me give an example with ordinary (not differential) equations.
>
> eq1:  x = y+3$
> eq2:  x*5=2*y-7$
>
> solve( [eq1, eq2], [x,y]);
>
> OR
>
> eqs: [ x = y+3,  x*5=2*y-7 ]$
> vars: [x,y]$
> solve(eqs,vars);
>
> You can do the same thing for systems of equations using 'makelist':
>
> eqs: makelist( x[ i ] = x[ i+1 ] + x[ i-1 ] + 1, i , 1, 5 )$
> solve(    append([x[0]=x[8],x[3]=1],eqs),      << add some extra equations
>              makelist(x[i],i,0,8));                       << list of
> variables
>
> I have not worked with the differential equation solvers for a long time,
> so I don't know whether they can solve your equations.
>
>            -s
>
>
>
>
> On Wed, Jan 12, 2011 at 22:46, razif razali <razif66 at gmail.com> wrote:
>
>>
>>
>> On Thu, Jan 6, 2011 at 9:40 PM, Leo Butler <l.butler at ed.ac.uk> wrote:
>>
>>>
>>>
>>> On Thu, 6 Jan 2011, razif razali wrote:
>>>
>>> < Thanks for your reply,
>>> < so from your guide, here what I come through,
>>> < ------------------
>>> < df(n,k):=
>>> < block ([],
>>> <     if n=0
>>> <     then 0
>>> <   else
>>> <
>>>   'diff(f[2*n,k],s)=x*((k-1)*sqrt(n-k+2)*f[2*n,k-1]-k*sqrt(n-k+1)*f[2*n,k+1])
>>> < );
>>> < makelist(df(1,k),k,1,2);
>>> < ------------------------
>>> < I can get the equation for diff( f[2,1],s) and diff( f[2,2],s)
>>> respectively,
>>> <
>>> < so next thing is, how can i make diff( f[2,1],s) and diff( f[2,2]) hold
>>> it value?because when I type again diff( f[2,1],s) in maxima after give code
>>> above, it gives
>>> < zero. what i want do here is after i get equation diff( f[2,1],s) i
>>> want to solve with both equation using ode method to get function of f[2,1]
>>> and f[2,2] with
>>> < f[2*n,k](0)=A, and value of x and A are not zero...
>>>
>>>  The problem is that Maxima does not know that f[n,k] is a function of
>>>  s, too. Here is a solution:
>>>
>>>  depends(f,s);
>>>  df[n,k] := if n=0 then 0 else
>>> diff(f[2*n,k],s)=x*((k-1)*sqrt(n-k+2)*f[2*n,k-1]-k*sqrt(n-k+1)*f[2*n,k+1]);
>>>  .
>>>  .
>>>  .
>>>  Note that I do not use 'diff, because the first line tells Maxima
>>>  that f is a function of s.
>>>
>>> Leo
>>> --
>>> The University of Edinburgh is a charitable body, registered in
>>> Scotland, with registration number SC005336.
>>>
>>> by telling MAXIMA that f[n,k] is function of s to helped me without using
>> 'diff but then it still not hold the function for next used?
>> the result still the same,
>>
>> depends(f,s);
>>  df[n,k] := if n=0 then 0 else
>> diff(f[2*n,k],s)=x*((k-1)*sqrt(n-k+2)*f[2*n,k-1]-k*sqrt(n-k+1)*f[2*n,k+1]);
>> makelist(df[1,k],k,1,2);
>>
>> then i got the diff(f [2,1],s) and diff( f[2,2],s)
>>
>> so how to make diff(f [2,1],s) and diff( f[2,2],s) hold its function so
>> that I can solve it using ODE in MAXIMA?because when i type all command
>> above and get the result, when i type again diff( f[2,1],s) it give
>> nothing...
>>
>>
>>
>>
>> --
>> Regards,
>>
>> RAZIF RAZALI,
>> Tutor & Master Student,
>> Physics Department,
>> Faculty Of Science,
>> Universiti Teknologi Malaysia(UTM).
>> +60199393606
>>
>>
>>
>>
>> _______________________________________________
>> Maxima mailing list
>> Maxima at math.utexas.edu
>> http://www.math.utexas.edu/mailman/listinfo/maxima
>>
>>
>


-- 
Regards,

RAZIF RAZALI,
Tutor & Master Student,
Physics Department,
Faculty Of Science,
Universiti Teknologi Malaysia(UTM).
+60199393606