       Re: problem

• To: mathgroup at smc.vnet.net
• Subject: [mg100330] Re: [mg100302] problem
• From: "David Park" <djmpark at comcast.net>
• Date: Mon, 1 Jun 2009 07:08:02 -0400 (EDT)
• References: <21606229.1243766725441.JavaMail.root@n11>

```Sometimes, in attempting to use DSolve or Solve, it helps to avoid
approximate numbers such as 0.5. So, I rewrote your differential equations
as follows (but it didn't help any with DSolve):

deqns = {y''[x] == -y[x]*((y[x])^2 + (z[x])^2)^(1/2),
z''[x] == -z[x]*((y[x])^2 + (z[x])^2)^(1/2), y' == 1, y == 1,
z' == 1/2, z == 1};

Clear[y, z];
dsols = First@NDSolve[deqns, {y, z}, {x, -100, 100}]
{y[x_], z[x_]} = {y[x], z[x]} /. dsols

ParametricPlot[{y[x], z[x]}, {x, -100, 100},
Frame -> True]

David Park
djmpark at comcast.net
http://home.comcast.net/~djmpark/

From: parmida shabestary [mailto:dj_poni at yahoo.com]

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' == 0.5, z == 1,
y == 1, z' == 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).