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