solving for variable and then get these e's..?

*To*: mathgroup at smc.vnet.net*Subject*: [mg46911] solving for variable and then get these e's..?*From*: sean_incali at yahoo.com (sean kim)*Date*: Sun, 14 Mar 2004 23:54:26 -0500 (EST)*Sender*: owner-wri-mathgroup at wolfram.com

Hello Group. I was playing around with lorenz system again. I assigned random numbers for all the parameters. and made a steady state system based on that and solved for the variables. and I get the following. ( the code is at the bottom) {y[0] == 0.1889025652295933*(-1.3382047869208344 - 0.47590327034877034*Sqrt[7.906927918602607 - 18.515309886236974*e]), x[0] == 0.31792235868739005*(1.5727110293983604 + 0.5593002876087739*Sqrt[7.906927918602607 - 18.515309886236974*e]), z[0] == 0.042970475451898735*(7.906927918602607 + 2.8119260158479644*Sqrt[7.906927918602607 - 18.515309886236974*e]} What are those little e's at the end of the solutions? Is that euler's number? and why can't I use that in NDSolve routine? are those signifcant? any thoughts are appreciated. In[270]:= ode = {x'[t]== -a y[t]-b z[t],y'[t]== c x[t]+d y[t], z'[t] == e-f z[t]+f x[t] z[t]} %/._'[t]->0 Solve[%,{x[t], y[t], z[t]}] %/.{a-> Random[Real, {1, 3}], b-> Random[Real, {1, 3}], c-> Random[Real, {1, 3}],d-> Random[Real, {1, 3}], d-> Random[Real, {1, 3}],f-> Random[Real, {1, 3}]}/.Rule ->Equal/.t-> 0 //InputForm s1 =% [[1]] s2 = %%[[2]] NDSolve[Join[{x'[t]\[Equal]-a y[t]-b z[t],y'[t]\[Equal]c x[t]+d y[t], z'[t]\[Equal]e-f z[t]+f x[t] z[t]}, s1], {x[t], y[t], z[t]}, {t, 0, 10}]