       Re: Can Mathematica solve this differential equation ?

• To: mathgroup at smc.vnet.net
• Subject: [mg107109] Re: Can Mathematica solve this differential equation ?
• From: "Nasser M. Abbasi" <nma at 12000.org>
• Date: Wed, 3 Feb 2010 06:08:43 -0500 (EST)
• References: <hk8nlh\$8h4\$1@smc.vnet.net>

```"Ashok" <nils_von_nostrand at yahoo.com> wrote in message
news:hk8nlh\$8h4\$1 at smc.vnet.net...
> 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
>

One way to solve the first ode and use its results as initial conditions for
the second ode?
Here is an example:

Clear[x,M1,M2,y1,y2]
M1=x;
M2=2 x;

First@DSolve[{y1''[x]==M1,y1==0,y1==1},y1[x],x];
y1=y1[x]/.%
Out= 1/6 (5 x+x^3)

First@DSolve[{y2''[x]==M2,y2==y1/.x->1,y2'==D[y1,x]/.x->1},y2[x],x];
y2=y2[x]/.%
Out= 1/3 (1+x+x^3)

--Nasser

```

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