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Re: Ploting integral curves

  • To: mathgroup at smc.vnet.net
  • Subject: [mg90010] Re: [mg89960] Ploting integral curves
  • From: Bob Hanlon <hanlonr at cox.net>
  • Date: Thu, 26 Jun 2008 04:43:27 -0400 (EDT)
  • Reply-to: hanlonr at cox.net

f[x_, y_] := 4 x y - x^4 - y^4

soln = Select[
  {x, y} /. Solve[{D[f[x, y], x] == 0, D[f[x, y], y] == 0}, {x, y}]=
,
  Element[#, Reals] &]

{{-1, -1}, {0, 0}, {1, 1}}

f @@@ soln

{2,0,2}

Plot3D[f[x, y], {x, -2, 2}, {y, -2, 2}]

d = 0.1;

Plot3D[f[x, y],
    {x, #[[1]] - d, #[[1]] + d},
    {y, #[[2]] - d, #[[2]] + d},
    ImageSize -> 400] & /@ soln // Column


Bob Hanlon

---- Barun von Doppeldecker <nikoi8888 at gmail.com> wrote:
> if you still want to help. here is another problem i came across today: i
have a function f(x, y) = 4xy =E2=88=92 x^4 =E2=88=92 y^4 and i have to d=
o three things.
First i have to find candidates for local extremes, then i have to exactly
pinpoint that extremes and finally plot a graf surrounding that point of
extremum.
I have found candidates, but the other two things i just can't....Here is
what i've done:

f[x_,y_]:=4 x y-x^4-y^4

*Solve[{D[f[x,y],x]**=C2=8A**0,D[f[x,y],y]**=C2=8A**0},{x,y}]*
if you could help me with other 2 things, i would be really grateful... if
not, thank you anyway.... ;)





On Wed, Jun 25, 2008 at 1:11 PM, Bob Hanlon <hanlonr at cox.net> wrote:

> soln = y[x] /. DSolve[4 x^2 + 2 y[x] y'[x] == 0, y[x], x]
>
> {(-Sqrt[2/3])*Sqrt[3*C[1] - 2*x^3],
>   Sqrt[2/3]*Sqrt[3*C[1] - 2*x^3]}
>
> Plot[soln /. C[1] -> 10, {x, -5, 3}]
>
>
> Bob Hanlon
>
> ---- noxon <nikoi8888 at gmail.com> wrote:
> > if anybody can give me some examples of ploting some integral curves, i
> > would be very gracious... for example: 4x^2+2yy'=0   ....how can i pl=
ot
> > that, i've tried everything but there is no curve....
> >
> >
> >
>
>




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