       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:=
m = 10^16;
mp = 1.2211*10^19;
G = mp^(-2);
V[\[Phi]_] := (1/2)*m^2*\[Phi][t]
\[Rho][\[Phi]_] :=
Derivative[\[Phi]][t]^2/2 +
V[\[Phi]]
H := Sqrt[((8*Pi*G)/3)*
\[Rho][\[Phi]]]

In:=
Inflaton :=
Derivative[\[Phi]][t] +
3*H*Derivative[\[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:=
f = \[Phi] /. First[NDSolve[
{Inflaton == 0,
Derivative[\[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[\[Phi]][x] would give the above, but not
the way I'm doing it.