In formation of differential equation of a given equation what are the things we should eliminate? I have read that if there are n number of arbitrary constants than the order of differential equation so formed will also be n. A question in my textbook says "Obtain the differential equation of all circles of radius a and centre (h,k) that is (x-h)^2+(y-k)^2=a^2." Now I don't know which one h, k or a should be eliminated or all should be eliminated etc.
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all h,k and a will be eliminated because they could assume any value which means they are arbitrary. If one of them has a constant non arbitrary value say a=1 then a would not be eliminated.
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$\begingroup$ Thanks that's what I thought but my book eliminated only h and k $\endgroup$ Sep 3, 2016 at 14:05
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$\begingroup$ Can you also tell why we need to eliminate arbitrary constants? Thanks $\endgroup$ Sep 3, 2016 at 14:06
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$\begingroup$ Because we need to make a differential equation of a class of curves that vary only in the value of arbitrary constant. $\endgroup$ Sep 3, 2016 at 14:17