Re: Can Mathematica solve this differential equation ?
- To: mathgroup at smc.vnet.net
- Subject: [mg107138] Re: Can Mathematica solve this differential equation ?
- From: JH <jlucio at ubu.es>
- Date: Wed, 3 Feb 2010 06:14:01 -0500 (EST)
- References: <firstname.lastname@example.org>
On 2 feb, 09:27, Ashok <nils_von_nostr... at yahoo.com> wrote: > In beam bending, we have the following situation: > > y '' [x] = M(x), boundary conditions specified for y and y > > Simple enough, but the problem arises as M is a piecewise-defined > function (linear in all pieces though) > > i.e., M(x) = M1(x) for 0<x<1 > and M(x) = M2(x) for 1<x<2 > M(x) = 0 for all other values of x > > Obviously, we are only interested in the interval 0<x<1 > > This leads to two separate equations: > > y1'' [x] = M1(x) in 0<x<1 > y2 '' [x] = M2(x) in 1 <x <2 > > Now we will have 4 constants of integration. We therefore need 4 > equations to solve for them. Two of them are obtained from the > specified boundary conditions for y and y. The other two come > from continuity equations: > y1 = y2 and y1 '  = y2 ' . It is these last two that > totally throw me off. I do not understand how to put them into > Mathematica. > > Any help is appreciated. > > Thank you > > Ashok Hi, Ashok, Why do you include the second domain (1<x<2) if you say 'Obviously, we are only interested in the interval 0<x<1'? I don't understand the reason for this last domain. Or else, could you give the particular forms of the functions M1(x) and M2(x), so that we can try to find a solution? Thanks. JH