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MathGroup Archive 2001

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Re: Mathematica 3.0, 4.0, 4.1 differences in DSolve[]

  • To: mathgroup at smc.vnet.net
  • Subject: [mg26670] Re: Mathematica 3.0, 4.0, 4.1 differences in DSolve[]
  • From: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>
  • Date: Wed, 17 Jan 2001 00:47:22 -0500 (EST)
  • Organization: Universitaet Leipzig
  • References: <93r9d2$52v@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

Hi,


the solution 

p[t]->ip - (Log[1 + (f^2*iv^2)/a] + 
   2*Log[Cos[Sqrt[a]*f*t + I/2*Log[1 - (I*f*iv)/Sqrt[a]] - 
       I/2*Log[1 + (I*f*iv)/Sqrt[a]]]])/(2*f^2)

is correct. It is easy obtained by lowering the order
of the equation and first solve p1'[t]==f^2*p1[t]+a

One finds that Mathematica 4.0.2 (with numerous error messages)
find thew correct solution also and the solution is correct.

Regards
  Jens
Paul Lutus wrote:
> 
> 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[0] == ip,p'[0] == 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.
> 
> Any comments?
> 
> --
> Paul Lutus
> www.arachnoid.com


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