differential



On 03/22/2013 06:03 PM, Thomas D. Dean wrote:
> On 03/22/13 07:04, Barton Willis wrote:
>
>> Try (your answer is nicer)
>>
>>   (%i1) depends(y,x)$
>>   (%i2) a*x + b*y+c=0$
>>   (%i3) [%,diff(%,x), p^2=c^2/(a^2+b^2)]$
>>   (%i4) eliminate(%,[a,b])$
>>   (%i5) factor(%);
>>   (%o5) 
>> [-c^2*x^2*(x^2*('diff(y,x,1))^2-p^2*('diff(y,x,1))^2-2*x*y*('diff(y,x,1))+y^2-p^2)]
>>
> Thanks, but,
> This does not eliminate c.
>

Hi Thomas,
I got a solution different from yours and similar to Barton's, but 
without c:

depends(y,x);
eq1: a*x+b*y=p$
eq2: a^2+b^2=1$
eq3: diff (eq1,x)$
eq4: first (eliminate  ([eq1,eq2,eq3], [a,b]));
[edo1,edo2]: solve (eq4, diff(y,x));

(%o7) ['diff(y,x,1) = (p*sqrt(y^2+x^2-p^2)+x*y)/(x^2-p^2),
        'diff(y,x,1) = -(p*sqrt(y^2+x^2-p^2)-x*y)/(x^2-p^2)]

Can you tell me the reference for the book you are using; I'm very 
interested in this subject

Regards,
Jaime