RE: Why these graphs differ?

*To*: mathgroup at smc.vnet.net*Subject*: [mg33953] RE: [mg33925] Why these graphs differ?*From*: "David Park" <djmp at earthlink.net>*Date*: Wed, 24 Apr 2002 01:22:11 -0400 (EDT)*Sender*: owner-wri-mathgroup at wolfram.com

Vladimir, The first plot is no good at all. The Mathematica iterator substitutes the numerical value of z into the DSolve statement and THEN evaluates DSolve. But by then the statement makes no sense, so you obtain error messsages. For example, when z -> 0.5 the DSolve statement is DSolve[{y'[0.5] == 0.5, y[0] == 1}, y[0.5], 0.5] which is no good at all. (I'm not certain why Mathematica gives any plot at all.) The second Plot statement works because the DSolve statement is evaluated first. Then the iteration is done. Generally, I would tend to do the differential equation solving first, and copy or define the resulting function, and then do the Plotting. Otherwise you are entangling two operations - each of which can present their own complications. David Park djmp at earthlink.net http://home.earthlink.net/~djmp/ > From: Vladimir Bondarenko [mailto:vvb at mail.strace.net] To: mathgroup at smc.vnet.net > > These solutions, naturally, coincide. > > DSolve[{y'[z] == z, y[0] == 1}, y[z], z][[1, 1, 2]] > Evaluate[DSolve[{y'[z] == z, y[0] == 1}, y[z], z][[1, 1, 2]]] > > (2 + z^2)/2 > (2 + z^2)/2 > > > But, surprisingly, the corresponding graphs are not identical: > > Plot[ DSolve[{y'[z] == z, y[0] == 1}, y[z], z][[1, 1, > 2]], {z, 0, 1}] > Plot[Evaluate[DSolve[{y'[z] == z, y[0] == 1}, y[z], z][[1, 1, > 2]]], {z, 0, 1}] > > > Is it a feature or a problem? > > > Vladimir Bondarenko > > >