Re: Re: PDE's with DSolve

*To*: mathgroup at smc.vnet.net*Subject*: [mg6055] Re: [mg6045] Re: [mg5983] PDE's with DSolve*From*: sherod at boussinesq.Colorado.EDU (Scott Herod)*Date*: Sun, 16 Feb 1997 01:11:57 -0500*Organization*: /usr/local/lib/rn/organization*Sender*: owner-wri-mathgroup at wolfram.com

Perhaps I am misunderstanding your comments. If so please forgive my explanation. When I say "Solve the differential equation F(x,y(x),y'(x)) = 0" I mean find the function y(x) such that F(x,y,y') is always zero on some set (interval) of x's. For many functions F there are standard ways to find such functions y(x). In the case of the problem that I asked Mathematica to solve (in easy notation) d^2 ---- y(x,t) = 0 (or y_{tt} = 0} dt^2 the true solution is y(x,t) = a(x) + b(x) * t where a and b are arbitrary functions of x. Mathematica on the otherhand returns y(x,t) = a(x) + b(t) which is wrong. If you ask Mma to solve y_{xt} = 0 it appears to return y = k x t + a(x) + b(t). I say appears because the actual result is {{y[x[1],x[2]]\[Rule]-DSolve`DSolveDump`b$12 x[1] x[2]+C[1][x[1]]+C[2][x[2]]}} ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ (??) At any rate this is also not correct. Scott Herod sherod at newton.colorado.edu ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ In article <5e0vt8$dlr at smc.vnet.net> "Christopher R. Carlen" <crobc at epix.net> writes: >Scott Herod wrote: >> >> I was happy to see that DSolve can solve some quasi-linear partial >> differential equations and was happily playing with it. I then tried >> the following: >> >> DSolve[D[y[x,t], {t,2}] == 0, y[x,t], {x,t}]. >> >> Rather distressing. >> >> Scott Herod > >Wouldn't it be necessary to have previously defined y[x,t] to be some >explicit function? > >In other words, I cannot possibly solve even > >F(x,y,y')=0 without having knowledge of the function y(x) . > >Once y(x) is defined, then I can consider the means to find a solution. > >_____________________ >Christopher R. Carlen >crobc at epix.net >carlenc at cs.moravian.edu >