       Re: Re: Ploting integral curves

• To: mathgroup at smc.vnet.net
• Subject: [mg90041] Re: [mg90010] Re: [mg89960] Ploting integral curves
• From: Bob Hanlon <hanlonr at cox.net>
• Date: Fri, 27 Jun 2008 06:15:52 -0400 (EDT)

```Somewhere in the e-mail process there was an unusual line wrap effect. Change to read

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

Bob Hanlon

---- Bob Hanlon <hanlonr at cox.net> wrote:
> 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, #[] - d, #[] + d},
>     {y, #[] - d, #[] + 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 - 2*x^3],
> >   Sqrt[2/3]*Sqrt[3*C - 2*x^3]}
> >
> > Plot[soln /. C -> 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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