*To*: mathgroup@smc.vnet.net*Subject*: [mg12124] Re: 1+Cos[x]Cosh[x]==0 ?*From*: "Stephen P Luttrell" <luttrell@signal.dra.hmg.gb>*Date*: Mon, 27 Apr 1998 01:46:09 -0400*Organization*: Defence Evaluation and Research Agency*References*: <6hpgug$djf@smc.vnet.net>

> >How to solve "1 + Cos[x] Cosh[x] == 0"? I will probably need just the >first five, positive solution of "x". > First of all plot out the left hand side in such a way that it is easy to estimate good starting points for each of the roots. The following input will do this for you Plot[Log[Abs[1 + Cos[x] Cosh[x]]] ,{x,0,15}] Select the plot, hold down CTRL (or whatever equivalent modifier key your system happens to use), and move the cursor around to read off the approximate coordinates of each root, and use these to construct the starting points in the following expression Map[FindRoot[1 + Cos[x] Cosh[x]==0,{x,#}]&,{1.78,4.64,7.74,11.0,14.1}] which evaluates to yield the output {{x -> 1.8751}, {x -> 4.69409}, {x -> 7.85476}, {x -> 10.9955}, {x -> 14.1372}} which solves your problem. ==================================================== Stephen P Luttrell luttrell@signal.dra.hmg.gb Adaptive Systems Theory 01684-894046 (phone) Room EX21, DERA 01684-894384 (fax) Malvern, Worcs, WR14 3PS, U.K. http://www.dra.hmg.gb/cis5pip/Welcome.html