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Differentiation to Solve Modified Sum of Binomial Coefficients

3. If x=asinp...

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3. If x=asinpt. y=bcospt Than show (a2 - x2)ydy2/dx2 + b2 = 0

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Q. If x = a sin pt, y = b cost p, then show that

(a^{2} - x^{2}) y \frac{d^{2} y}{d x^{2}} + b^{2} = 0.

(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

If, for some prove that

is a constant independent of a and b.

(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

y = log [x + \sqrt{x^{2} + a^{2}}]

(x^{2} + a^{2}) \frac{d^{2} y}{d x^{2}} + x \frac{d y}{d x} = 0

.

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Differentiation to Solve Modified Sum of Binomial Coefficients

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