       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: <hk8nlh\$8h4\$1@smc.vnet.net>

```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

```

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