how can I solve my system of differential equations?

*To*: mathgroup at smc.vnet.net*Subject*: [mg132116] how can I solve my system of differential equations?*From*: raj <pianoman2012sg at gmail.com>*Date*: Thu, 12 Dec 2013 01:28:20 -0500 (EST)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com*Delivered-to*: l-mathgroup@wolfram.com*Delivered-to*: mathgroup-outx@smc.vnet.net*Delivered-to*: mathgroup-newsendx@smc.vnet.net

hi guys, I have a question pertaining to my code below: for a problem that i'm working on, I require to find the values of the roots E2 that will set the function f1[E2] - f2[E2] to zero. I know how to obtain the roots one at a time: for instance finding a a root of E2 lying between, say 0 and 2. But I would like to know whether it is possible to get Mathematica to generate all the roots that lie within a certain interval at once, say all the possible ones lying between say 0 and 10. I have tried using NSolve and Reduce, but I got nothing out of them , so any help in refining the code to do this will be most appreciated! regards raj n xmin = -6.500; xmax = 6.500; xmatch = 1.50; eq1[x_, x0_, E2_] := (y''[x]) + (E2 - x^2) y[x] == 0, y[x0] == 0, Derivative[1][y][x0] == 1/10^6}; y1[x_, E2_] := y[x] /. NDSolve[eq1[x, xmin, E2], y, {x, xmin, xmatch}][[1]]; f1[E2_] := Abs[\!\( \*SubscriptBox[\(\[PartialD]\), \(x\)]\ \(y1[x, E2]\)\)/ y1[x, E2] /. x -> xmatch]; y2[x_, E2_] := y[x] /. NDSolve[eq1[x, xmax, E2], y, {x, xmax, xmatch}][[1]]; f2[E2_] := Abs[\!\( \*SubscriptBox[\(\[PartialD]\), \(x\)]\(y2[x, E2]\)\)/y2[x, E2] /. x -> xmatch] f[E2_?NumericQ] := f1[E2] - f2[E2]; NSolve[f[E2_?NumericQ] == 0 && 0 < E2 < 10, E2] rts = Reduce[f == 0 && 2.5 < E2 < 10.0, E2] c2 = N[E2 /. {ToRules[rts]}] Print["The value of E2 was=", c2]