Re: problem

*To*: mathgroup at smc.vnet.net*Subject*: [mg100346] Re: problem*From*: "Sjoerd C. de Vries" <sjoerd.c.devries at gmail.com>*Date*: Mon, 1 Jun 2009 07:11:00 -0400 (EDT)*References*: <gvtmio$gic$1@smc.vnet.net>

Hi Parmida, If you examine your two equations you see that they are actually identical. If you swap z and y you get the same equations. Conclusion:the solutions for z and y must be the same either. y[x]==z [x]. You can therefore replace z in the first equation with y and solve for y only. DSolve[y''[x] == -y[x] Sqrt[(y[x]^2)]*Sqrt[2], y[x], x] It is still a difficult nut to crack though. Mathematica finds a result in the form of an integral equation, which doesn't help you much. Cheers -- Sjoerd On May 31, 12:36 pm, parmida shabestary <dj_p... at yahoo.com> wrote: > Hi > I'm having trouble solving this set of equations: > > y''[x] =-y[x]*((y[x])^2 + (z[x])^2)^0.5 > z''[x] =-z[x]*((y[x])^2 + (z[x])^2)^0.5 > > I couldn't write a DSolve order for it but here is the numerical code I wrote: > > NDSolve[{y''[x] == -y[x]*((y[x])^2 + (z[x])^2)^0.5, > z''[x] == -z[x]*((y[x])^2 + (z[x])^2)^0.5, y'[0] == 0.5, z[0]= == 1, > y[0] == 1, z'[0] == 0.5}, {y, z}, {x, -100, 100}] > > I can plot this answer but what I really need is the parametric solution(a set of equations for z and y depending on x). > > Please help me find the answer. > > thanx > parmida