The value is=?

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1 Answer
Mar 15, 2018

Answer is (4).

Explanation:

y=(x+x21)15+(xx21)15

Hence dydx=15(x+x21)14(1+2x2x21)+15(xx21)14(12x2x21)

= 15(x+x21)14(1+xx21)+15(xx21)14(1xx21)

= 15(x+x21)14(x21+xx21)+15(xx21)14(x21xx21)

= 15(x+x21)15x2115(xx21)15x21

or x2115dydx=(x+x21)15(xx21)15

and similarly we have

x2115d2ydx2+dydx2x30x21=15(x+x21)15x21+15(xx21)15x21

or x21225d2ydx2+dydxx225=(x+x21)15+(xx21)15=y

or (x21)d2ydx2+xdydx=225y

Hence answer is (4).

Additional Information Observe that for y=(x+x21)n+(xx21)n, (x21)d2ydx2+xdydx would be n2y