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).
>