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Re: Ploting integral curves
*To*: mathgroup at smc.vnet.net
*Subject*: [mg89992] Re: Ploting integral curves
*From*: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>
*Date*: Thu, 26 Jun 2008 04:40:02 -0400 (EDT)
*Organization*: The Open University, Milton Keynes, UK
*References*: <g3t6p6$ihk$1@smc.vnet.net>
noxon 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 plot
> that, i've tried everything but there is no curve....
(* First, we write the differential equation with correct Mathematica
syntax. *)
de = 4 x^2 + 2 y[x] y'[x] == 0;
(* Then, we solve it thanks to the DSolve[] function. *)
sols = DSolve[de, y[x], x];
(* Since we have two solutions -- one family of functions below the
x-axis and the other one above the x-axis, we build two expressions to
be plotted. *)
f1 = y[x] /. sols[[1]] /. C[1] -> C1;
f2 = y[x] /. sols[[2]] /. C[1] -> C1;
(* Finally, we plot a sample of the family of functions. *)
Plot[Table[{f1, f2}, {C1, -2, 2}], {x, -3, 2}, ImageSize -> 500,
PlotStyle -> Thick]
Regards,
-- Jean-Marc
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