Re: 2nd order differential equation help

*To*: mathgroup at smc.vnet.net*Subject*: [mg31525] Re: 2nd order differential equation help*From*: BobHanlon at aol.com*Date*: Fri, 9 Nov 2001 06:13:28 -0500 (EST)*Approved*: Steven M. Christensen <steve@smc.vnet.net>, Moderator*Sender*: owner-wri-mathgroup at wolfram.com

In a message dated 2001/11/7 7:48:34 AM, peterangelo at mindspring.com writes: >actly how do I get this into a form Mathamatica will accept? It has >been a number of years since enrolling in diffeq, however I think I am >close to correct but would appreciate help. > >the problem; > >Solve the differential equation: > >g''(t) + 0.1 g'(t) + g(t) = 0 > >where the previous equation uses conventional mathematical notation. >You must transfrom the equation and initial conditions into >Mathematica syntax. > >for t between 0 and 10 Pi > >subject to the initial conditions > g(0) = 0, > g'(0) = 1 > >Plot your results. > >My attempt is as follows: > > >Clear[g] > >Clear[eqn] > >eqn[t_] = g''[t] + 0.1g'[t] + g[t] == 0 > > >Clear[eqn1] > >eqn1[t_] = g'[t] + 0.1g[t] + ?g[t] == 0 > >solution = DSolve[{eqn[t], eqn1[t]}, g'[0] == 1, >g[0] == 0, g[t], {t, 0, 10\[Pi]}] > >DSolve::dsvar: g[0]==0 cannot be used as a variable. > >what am I dont doing right? any suggestions helpful > Clear[g]; g[t] /. DSolve[{g''[t]+g'[t]/10+g[t]==0, g[0] == 0, g'[0] == 1}, g[t], t][[1]] (10*I*(E^((1/20)*(-1 - I*Sqrt[399])* t) - E^((1/20)*(-1 + I*Sqrt[399])*t)))/Sqrt[399] ExpToTrig [%] (10*I*Cosh[(1/20)*(-1 - I*Sqrt[399])*t])/Sqrt[399] - (10*I*Cosh[(1/20)*(-1 + I*Sqrt[399])*t])/Sqrt[399] + (10*I*Sinh[(1/20)*(-1 - I*Sqrt[399])*t])/Sqrt[399] - (10*I*Sinh[(1/20)*(-1 + I*Sqrt[399])*t])/Sqrt[399] FullSimplify[%] (20*Sin[(Sqrt[399]*t)/20])/ (E^(t/20)*Sqrt[399]) Consolidating these steps into a definition for g[t] g[t_] := Evaluate[FullSimplify[ ExpToTrig[g[t] /. DSolve[{g''[t]+g'[t]/10+g[t]==0, g[0] == 0, g'[0] == 1}, g[t], t][[1]]]]]; Checking g''[t]+g'[t]/10+g[t] == 0 // Simplify True Plot[g[t], {t, 0, 10Pi}]; Bob Hanlon Chantilly, VA USA