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