If x-a2-y-b2-c2- for some c-0- prove that -1-d y-d x2-3-2-d2 y-d x2 is a constant independent of a and b-

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If x-a2+y-b2=...

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If, for some prove that

is a constant independent of a and b.

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(x - a)^{2} + (y - b)^{2} = c^{2}

\frac{{[1 + {(\frac{d y}{d x})}^{2}]}^{3 / 2}}{\frac{d^{2} y}{d x^{2}}}

C

(x - a)^{2} + (y - b)^{2} = c^{2}

\frac{{[1 + {(\frac{d y}{d x})}^{2}]}^{\frac{3}{2}}}{\frac{d^{2} y}{d x^{2}}} = c o n s t a n t

y = x^{x}

\frac{d^{2} y}{d x^{2}} - \frac{1}{y} {(\frac{d y}{d x})}^{2} - \frac{y}{x} = 0.

{[1 + {(\frac{d y}{d x})}^{2}]}^{3} = C^{2} {[\frac{d^{2} y}{d x^{2}}]}^{2}

y = (c_{1} c o s (x + c_{2})) - (c_{3} e^{(- x + c_{4})}) + (c_{5} s i n x)

c_{1}, c_{2}, c_{3}, c_{4}, c_{5}

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