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Re: problem

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'[0] == 1, y[0] == 1,
    z'[0] == 1/2, z[0] == 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  

From: parmida shabestary [mailto:dj_poni at] 

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
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.

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