This is Maple's attempt at solving the ODE in Equation (14)

> restart;

> s:=diff(Xi(xi),xi);

> t:=diff((s*xi),xi);

> eq1:=(1/xi)*t+(c^2)*(1-xi^2)*Xi(xi)=0;

This is Equation (14) - I'm using dsolve with only the 2nd boundary condition here because entering them both gives an error.

> p:=dsolve({eq1,D(Xi)(1)=0,D(Xi)(0)=0},Xi(xi));

> p:=dsolve({eq1,D(Xi)(1)=0},Xi(xi));

This is the solution following the imposition of one boundary condition.

> assign(p);Xi:=unapply(Xi(xi),xi);

Now I'm going to try to apply the second boundary condition after the fact.

> v:=diff(Xi(xi),xi)=0;

> xi:=0;

> solve(v,_C1);

Error, division by zero

Error, division by zero

BACK