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 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