RE: Why these graphs differ?

• To: mathgroup at smc.vnet.net
• Subject: [mg33946] RE: [mg33925] Why these graphs differ?
• From: "DrBob" <majort at cox-internet.com>
• Date: Wed, 24 Apr 2002 01:21:57 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

```The first form (without Evaluate) is not explicitly a function of z ---
where z appears in the expression, it is actually a dummy variable.
Plot holds its first argument unevaluated, so there's no unbound "z" in
the function expression to match the iterator in Plot.  Even if the
first form DID work for you, it would be horrifically slow, as DSolve
would be invoked repeatedly, for each point in the Plot.

"Unless otherwise specified, f is not evaluated until a specific value
has been assigned to i, and is then evaluated for each value of i
chosen. You can use Evaluate[f] to make f be evaluated immediately,
rather than only after a specific value has been assigned to i."  (A.4.2
under Help for Plot)

Bobby Treat

-----Original Message-----
From: Vladimir Bondarenko [mailto:vvb at mail.strace.net]
To: mathgroup at smc.vnet.net
Subject: [mg33946] [mg33925] Why these graphs differ?

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?