Re: Transforming an initial condition of a solved ODE into a new

*To*: mathgroup at smc.vnet.net*Subject*: [mg93490] Re: Transforming an initial condition of a solved ODE into a new*From*: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>*Date*: Tue, 11 Nov 2008 07:46:14 -0500 (EST)*Organization*: Uni Leipzig*References*: <gf8rep$pmp$1@smc.vnet.net>*Reply-to*: kuska at informatik.uni-leipzig.de

Hi, the function below woud give you y[tmax][x[0]] .. myY[x0_,tmax_:Pi]:=(y[t] /. NDSolve[{y'[t]==y[t]+x[t],x'[t]==-x'[t],x[0]==x0,y[0]==0},{y[t],x[t]},{t,0,tmax}])/. t->tmax Regards Jens Itzhak wrote: > I solved a two-variable(x[t],y[t]) second-order ODE. Now I wish to transform one initial condition of the problem (x[0]) into a variable, so that I can compute the following (which I give here symbolically to convey my intention): > > 1) Plot[y'[tmax][x[0]],{x[0],0,100}] > 2) NIntegrate[y'[tmax][x[0]],{x[0],0,100}] > > How can this be done? > > Thank you >