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

Question

If, for some prove that

is a constant independent of a and b.

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Solution

It is given that,

Differentiating both sides with respect to x, we obtain

Hence, proved.

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Similar questions

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

, then prove that

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

is a independent of

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.

Q. The differential equation

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

Q. The differential equation whose general solution is given by,

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}

are arbitrary constants, is

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