       Mathematica 3.0, 4.0, 4.1 differences in DSolve[]

• To: mathgroup at smc.vnet.net
• Subject: [mg26642] Mathematica 3.0, 4.0, 4.1 differences in DSolve[]
• From: "Paul Lutus" <nospam at nosite.com>
• Date: Sat, 13 Jan 2001 22:36:18 -0500 (EST)
• Sender: owner-wri-mathgroup at wolfram.com

```Dear Group:

When I upgraded to Mathematica 4.0, I promptly tested DSolve[] using one of
my favorite "tough" differential equations:

DSolve[{p''[t] == a+(p'[t] f)^2,p == ip,p' == iv},p,t]

The idea of the equation is to mimic the behavior of a mass falling under
the influence of gravity and affected by air resistance, which varies as the
square of velocity.

ip = initial position
iv = initial velocity
a = gravitational acceleration, usually a negative value when numerical
values are assigned
f = air resistance coefficient

To my surprise, version 4.0 solved it. Then version 4.1 arrived, and could
not solve it. Here is the history:

Version 3.0 could not solve this equation.
Version 4.0 could solve it, providing a rather complex but seemingly correct
result that graphs as one would expect.
Version 4.1 cannot solve it.

I am  mystified by this outcome. It *could* mean (1) the solution provided
by 4.0 was valid but changes in 4.1 prevent it, or (2) the 4.0 solution was
an error that should not have been permitted, and this was corrected in 4.1.

--
Paul Lutus
www.arachnoid.com

```

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