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.... > > > > > > > >