How to express ODE?

*To*: mathgroup at smc.vnet.net*Subject*: [mg52817] How to express ODE?*From*: Adam Getchell <agetchell at physics.ucdavis.edu>*Date*: Mon, 13 Dec 2004 04:24:15 -0500 (EST)*Sender*: owner-wri-mathgroup at wolfram.com

Still (unfortunately) not getting another ODE to work, even using Dr. Bob's example. I want to express this equation: In[143]:= m = 10^16; mp = 1.2211*10^19; G = mp^(-2); V[\[Phi]_] := (1/2)*m^2*\[Phi][t] \[Rho][\[Phi]_] := Derivative[1][\[Phi]][t]^2/2 + V[\[Phi]] H := Sqrt[((8*Pi*G)/3)* \[Rho][\[Phi]]] In[149]:= Inflaton := Derivative[2][\[Phi]][t] + 3*H*Derivative[1][\[Phi]][ t] + D[V[\[Phi]], \[Phi]] That is, phi double-dot of t + 3 H phi dot of t + V' of phi, where phi is a function of t; V is a function of phi; H is a function of rho; rho is a function of phi dot and V. However, solving Inflaton for phi as a function of t: In[163]:= f = \[Phi] /. First[NDSolve[ {Inflaton == 0, Derivative[1][\[Phi]][ t] == 0}, \[Phi], {t, 0, 100*m}]] Generates NDSolve::overdet and ReplaceAll::reps. I *think* part of my problem is that dV/d(phi) is not getting properly evaluated (it returns 0 when I look at it explicitly). I thought that Derivative[1][\[Phi]][x] would give the above, but not the way I'm doing it. --Adam