Plot3D with NDSolve

*To*: mathgroup at smc.vnet.net*Subject*: [mg81643] Plot3D with NDSolve*From*: sean_incali <sean_incali at yahoo.com>*Date*: Sun, 30 Sep 2007 04:02:04 -0400 (EDT)

Hello group, Let's say I can solve the following DE that depends on 2 paparmeters a and b, and plot it accordingly. eqn = y'[x] == b/(a y[x]) par = {a -> 1, b -> 1} solution = NDSolve[{eqn /. par, y[0] == 0.1}, y, {x, 0.1, 5}]; Plot[y[x] /. solution, {x, 0.1, 5}]; Above shows a 2d graph in x and y axes. What I want to do is now use one of the parameter as z axis. So I need to solve the DE while varying a from 1 to 5 for instance. Then I want to graph the solutions as a 3D object. with x. y and a axis (where a will be the new z axis.) I guess I can use Table to iterate the whole procedure, but I wanted to see how others would approach it. For instance, if I use eqn = y'[x] == b/(a y[x]) par = {b -> 1} solution = Table[NDSolve[{eqn /. par, y[0] == 0.1}, y, {x, 0.1, 5}], {a, 1, 5}]; Plot[Evaluate[y[x] /. solution], {x, 0.1, 5}]; It will shows all the solutions in one 2D graph. I want to see them in 3D. On the side note.. Why does the Plot require the "Evaluate" in the second code I posted and not in the first code??? If someone can explain that that will be great also. Thanks in advance as usual. sean