DSolve with recursively defined equations

*To*: mathgroup at smc.vnet.net*Subject*: [mg53760] DSolve with recursively defined equations*From*: pdickof at sasktel.net*Date*: Wed, 26 Jan 2005 04:37:21 -0500 (EST)*Sender*: owner-wri-mathgroup at wolfram.com

DSolve can handle this.... eq[0] = n0'[d] == -r n0[d]; eq[1] = n1'[d] == r(n0[d] - n1[d]); eq[2] = n2'[d] == r(n1[d] - n2[d]); in[0] = n0[0] == 1; in[1] = n1[0] == 0; in[2] = n2[0] == 0; eqns = Flatten[Table[{eq[i], in[i]}, {i, 0, 2}]]; funcs = {n0[d], n1[d], n2[d]}; DSolve[eqns, funcs, d] ...but when I try to generalize to the following ... Remove[nn, eq, in, eqns, funcs]; iCount=2; eq[0] = nn'[0, d] == -r nn[0, d]; eq[i_] := nn'[i, 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] ...I get the message DSolve::bvnul: For some branches of the general solution, \ the given boundary conditions lead to an empty solution. I don't understand the difference. Is it possible to generalize as above? Is it possible to obtain a general solution for the ith equation? What are the relevant sections in the documentation? Thanks in advance..... Peter Dickof

**Follow-Ups**:**Re: DSolve with recursively defined equations***From:*DrBob <drbob@bigfoot.com>