Re: ODE's

• To: MathGroup at yoda.physics.unc.edu
• Subject: Re: ODE's
• From: Mathematica Account <mma at mathematics.edinburgh.ac.uk>
• Date: Tue, 5 Jan 93 17:26:49 GMT

```On 10 Dec I posted the following:

>Can anyone see why the following set of two second order d.e.'s with
>constant coefficients fails (after a substantial amount of
>computation)?
>
>  DSolve[{6 x''[t]+n^2 (4 x[t]-2y[t])==0,6y''[t]+n^2(-3 x[t]+3
> y[t])==0,x[0]==0,x'[0]==0,y[0]==0,y'[0]==p/(3 m)},

1. Allan Hayes (hay at uk.ac.le) pointed out that the problem could be
worked round by recasting the equations as a system of 4 first-order
equations.

2. Brian Evans (evans at edu.gatech.eedsp.gauss) gave another, simpler,
example of failure:

DSolve[ 3 y'[t] + 4000 y[t] == 100 Cos[1000 t], y[t], t]

He pointed out that DSolve calls Simplify, which hangs on the
solution:
Simplify[ -2/(125*E^((4000*t)/3)) +
(2*((1/2 + (3*I)/8)*E^(-1000*I*t) + (1/2 - (3*I)/8)*E^(1000*I*t)))/125 ]

He has already reported this, but it may be a different problem from
the one I encountered. Mathematica returns my problem, unsolved, after
substantial calculation; but it hangs on Brian's DE.

Thanks to my respondents.

D.C. Heggie,
University of Edinburgh,
Dept. of Maths. & Stats.,
King's Buildings,
Edinburgh EH9 3JZ,
U.K.

Tel. (031-)650 5035
Fax  (031-)650 6553

```

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