Re: Plotting a series of Roots

*To*: mathgroup at smc.vnet.net*Subject*: [mg128800] Re: Plotting a series of Roots*From*: William Duhe <wjduhe at loyno.edu>*Date*: Tue, 27 Nov 2012 03:31:49 -0500 (EST)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com*Delivered-to*: l-mathgroup@wolfram.com*Delivered-to*: mathgroup-newout@smc.vnet.net*Delivered-to*: mathgroup-newsend@smc.vnet.net

So here I have an algorithm that gives me how my roots change as a function of lambda or t1[lambda,1]: s1[lambda_, t_] = x[t] /. DSolve[{x'[t] == lambda, x[0] == 0}, x[t], t][[1]]; lambda t; t1[lambda_, value_] = t /. Solve[s1[lambda, t] == value, t][[1]]; value/lambda; s1[lambda, t1[lambda, value]]; value; Plot[t1[lambda, 1], {lambda, .1, 1}, PlotRange -> Automatic] What I would like to do is in a similar fashion solve the differential equation bellow and plot how a particular root of that equation changes with \[Alpha]. It is important to note here that I have to use NDSolve rather than DSolve for this type of equation.What I would like is analogous to the above code modified to be t1[\[Alpha],1]with the modified equations. M = 10000; g = 1; \[Alpha] = 1; A = 10; a = .01;(*initial plot temp*) b = 1.2; (*final plot temp*) c = 0.00000001; (*initial temp*) d = 0; (*initial \[Beta]*) m = 1; bb = (g/(2*\[Pi])^(3/2)*(m/T)^(3/2)*E^(-m/T)); s = NDSolve[{\[Beta]'[T] == (3*\[Alpha]^2*M*T^(5/2))/( Sqrt[2*g]*m^(9/2))*(bb^2 - \[Beta][T]^2), \[Beta][c] == d}, \[Beta], {T, a, b}, Method -> "BDF"];

**Follow-Ups**:**Re: Plotting a series of Roots***From:*Bob Hanlon <hanlonr357@gmail.com>