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MathGroup Archive 2005

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Re: DSolve with recursively defined equations

  • To: mathgroup at smc.vnet.net
  • Subject: [mg53793] Re: DSolve with recursively defined equations
  • From: pdickof at sasktel.net
  • Date: Thu, 27 Jan 2005 05:41:37 -0500 (EST)
  • References: <ct7psr$ld$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

DrBob solved my problem:

>The problem is that the expressions nn'[0, d] and nn'[i, d] don't make
any >sense. Try this instead:

>Clear[nn, eq, in, eqns, funcs];
>iCount = 2;
>eq[0] = D[nn[0, d], d] == -r nn[0, d];
>eq[i_] := D[nn[i, d], d] == r(nn[i - 1, d] - nn[i, d]);
>in[0] = nn[0, 0] == 1;
>in[i_] := nn[i, 0] == 0;
>eqns = Flatten[Table[{eq[i], in[i]}, {i, 0, iCount}]]
>funcs = Table[nn[i, d], {i, 0, iCount}]
>DSolve[eqns, funcs, d]

which works (Thank-you!). The second part of the problem is still
unresolved. I happen to know that the solution to the ith function is
nn[n_,d_] := Exp[-d r ] Sum[(r d)^i / i!, {i,0,n-1}]
How would I go about getting this general form in Mathematica?

Peter


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