Implicit differentiation question



All,

This is really more a Maxima procedure question than one about implicit
differentiation. I would like to solve for d^2y/dx^2 ind the following
equation.

 

(%i1) eqn:x^2+y^2=r^2; 

(%o1) y^2+x^2=r^2

 

(%i2) depends(y,x);

(%o2) [y(x)]

 

(%i3) d1:diff(eqn,x);

(%o3) 2*y*('diff(y,x,1))+2*x=0

 

(%i4) solve(d1,'diff(y,x));

(%o4) ['diff(y,x,1)=-x/y]

 

(%i5) d2:diff(eqn,x,2);

(%o5) 2*y*('diff(y,x,2))+2*('diff(y,x,1))^2+2=0

 

(%i6) subst(%o4,'diff(y,x),%o5);

(%o6)
[2*y*('diff(y,x,2))+2*('diff(y,x,1))^2+2=2*y*('diff(y,x,2))+(2*x^2)/y^2+2]=0

 

(%i7) solve(%o6,'diff(y,x,2));

(%o7) []

 

I suspect my syntax in %i7. I appreciate the help

 

Ron