Temperature Distribution in a rod connecting two heat sources

Now we apply the simplification of fixing the temperature so that the temperature at x@0 and x@2L are equal.  This can be achieved with two heat sources.

> restart;

Start with the general equation as always.

> Theta:=x->M*exp(-m*x)+N*exp(m*x);

Set the equations for the endpoints, and equate them to solve for the M and N.

> eqn1:=Theta[0]=Theta(0);
eqn2:=Theta[0]=Theta(2*L);

> s:=solve({eqn1,eqn2},{M,N});

> assign(s);

> theta:=simplify(Theta(x)):
Theta:=unapply(theta,x):

This is our general equation with the constants solved for.

> Theta(x);

The temperature at the midpoint.

> Theta(L);

The temperature minimum (@L) can be reduced to a simple equation.

> bookans:=Theta[0]*(2/(exp(-m*L)+exp(m*L)));

> convert(bookans,trig);

> difference:=simplify(Theta(L)-bookans);