Re: changing variables in differential equations

*To*: mathgroup at smc.vnet.net*Subject*: [mg100647] Re: changing variables in differential equations*From*: dh <dh at metrohm.com>*Date*: Wed, 10 Jun 2009 05:34:10 -0400 (EDT)*References*: <h0l48t$opp$1@smc.vnet.net>

Hi Andre, having clearified that v= V[u] is to be considered the new dependent variable there is still the question if the dependent variable remains essentially the same or not: x=X[u,v[u]] y=Y[u,v[u]]= V[u] = v Anyway, we can define the i-derivative of y with respect to x by y[i] (note: lower case= variables, upper case= functions): ========================== Clear[x,X,y,Y]; x[0] = X[u, v[u]]; y[0] = Y[u, v[u]]; y[i_] := Dt[y[i - 1]]/Dt[x[0]] =========================== here is a simple example where the transformation only depends on u: ========================== X[u_, v_] := u^2; Y[u_, v_] := X[u, v] + X[u, v]^2 y[1]//Simplify ========================== Daniel Andre Hautot wrote: > Hello, > Given an ordinary differential equation of order n, H(x,y,y',y'',...)=0 > Given the change of variables : x=x(u,v) and y=y(u,v) > How to calculate (hopefully recursively) y', y'', and so on as functions > of say : u, v', v'' > > In other words how to translate automatically the differential equation > in terms of the new variables ? > Thanks in advance