differential



On 03/22/13 13:53, Thomas D. Dean wrote:

>
> I think the solution must have a 'diff(y,x,2) term.
>

OOPS!

'diff(y,x,1)^2

The solution given in the book is

[(y+r)^2*('diff(y,x,1))^2+y^2+2*r*y = 0,
         (y-r)^2*('diff(y,x,1))^2+y^2-2*r*y = 0]

I am close, the difference being the coefficient of the
'diff(y,x) term.  I am dropping a solution somewhere.


kill(all);
eq1:(x-h)^2+(y-k)^2=r^2;
eq2:subst(k=r,eq1);
depends(y,x);
eq3:solve(eq2,h);
load(to_poly_solve);
/* first solution */
eq4:subst(eq3[1],diff(eq2,x));
eq5:first(first(to_poly_solve(eq4,2*(y - r)*'diff(y,x)))^2/4);
eq6:lhs(eq5)-rhs(eq5)=0;
/* second solution */
eq7:subst(eq3[2],diff(eq2,x));
eq8:first(first(to_poly_solve(eq7,2*(y - r)*'diff(y,x)))^2/4);
eq9:lhs(eq8)-rhs(eq8)=0;

Tom Dean