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Student Support Forum: 'Basic ODE's not solveable in 5.0?!?' topicStudent Support Forum > General > "Basic ODE's not solveable in 5.0?!?"

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Author Comment/Response
Adam Getchell
12/12/04 8:36pm

Why would something simple:

DSolve[{Derivative[2][x][t] == (-Subscript[\[Omega], 0]^2)*
x[t], x[0] == x0, Derivative[1][x][0] == v0}, x,
t]

Fail with:

\!\(\*FormBox[
RowBox[{\(DSolve::"bvfail"\), \(\(:\)\(\ \)\), "\<\"For some branches of
the general solution, unable to solve
the conditions. \\!\\(\\*ButtonBox[\\\"More\\\", \
ButtonStyle->\\\"RefGuideLinkText\\\", ButtonFrame->None, \
ButtonData:>\\\"DSolve::bvfail\\\"]\\)\"\>"}], TraditionalForm]\)

Whereas:

In[194]:=
sol1 = DSolve[
Derivative[2][x][t] ==
(-Subscript[\[Omega], 0]^2)*
x[t], x, t]

Works just fine.

I am just having terrible trouble with ODE's that should be straightforward. Another example:

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]]

In[163]:=
f = \[Phi] /. First[NDSolve[
{Inflaton == 0,
Derivative[1][\[Phi]][
t] == 0}, \[Phi],
{t, 0, 100*m}]]

Gives:

NDSolve::overdet: There are fewer dependent variables, {ϕ(t)}, than
equations, so the system is overdetermined.

and ReplaceAll::reps (I can't copy the error message due to all the associated garbage. Another fun issue, since I *could* copy the previous message fine.)

This is incredible frustrating.




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