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