Re: DSolve Question

*To*: mathgroup at smc.vnet.net*Subject*: [mg50600] Re: [mg50589] DSolve Question*From*: Bob Hanlon <hanlonr at cox.net>*Date*: Sun, 12 Sep 2004 04:42:11 -0400 (EDT)*Reply-to*: hanlonr at cox.net*Sender*: owner-wri-mathgroup at wolfram.com

eq1=y''[t]+w^2 y[t]==0; initial={y[0]==y0,y'[0]==v0}; Table[(y[t] /. DSolve[{eq1,initial},y[t],t][[1,1]]) , {v0,0,2, 1/2}] // ColumnForm y0*Cos[t*w] (2*w*y0*Cos[t*w] + Sin[t*w])/(2*w) (w*y0*Cos[t*w] + Sin[t*w])/w (2*w*y0*Cos[t*w] + 3*Sin[t*w])/(2*w) (w*y0*Cos[t*w] + 2*Sin[t*w])/w This leads to the supposition that supp = y[t] -> (w*y0*Cos[t*w]+v0*Sin[t*w])/w; Verifying that this satisfies both the equation and the initial conditions Simplify[eq1 /. NestList[D[#,t]&,supp,2]] True initial == Drop[Equal@@#& /@ Simplify[NestList[D[#,t]&,supp,2] ,t==0],-1] True Bob Hanlon > > From: "John Reed" <nospamjreed at alum.mit.edu> To: mathgroup at smc.vnet.net > Date: 2004/09/11 Sat AM 06:44:49 EDT > To: mathgroup at smc.vnet.net > Subject: [mg50600] [mg50589] DSolve Question > > I'm relatively new to Mathematica, and I'm having trouble with a simple DE. > This is from Zimmerman & Olness, "Mathematica for Physics". Here's the > equation: > > eq1 = y''[t] + w^2 y[t] == 0 > > initial = {y[0] == y0, y'[0] == v0} > > eq3 = DSolve[{eq1, initial}, y[t], t] > > When this executes, I get the error message bvnul: For some branches of the > general solution, the given boundary conditions lead to an empty solution. > > Now, if I change v0 to a number, everything works fine. I've tried making > v0 real and positive, but with no luck. > > Any help is appreciated. > > John Reed > >