Can Mathematica solve this differential equation ?

• To: mathgroup at smc.vnet.net
• Subject: [mg107076] Can Mathematica solve this differential equation ?
• From: Ashok <nils_von_nostrand at yahoo.com>
• Date: Tue, 2 Feb 2010 03:27:41 -0500 (EST)

```In beam bending, we have the following situation:

y '' [x] = M(x), boundary conditions specified for y[0] and y[1]

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[0] and y[1]. The other two come
from continuity equations:
y1[1] = y2[1] and y1 ' [1] = y2 ' [1].  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

```

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