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Question

IfY=(x+x21)mshowthat
(x21)d2ydx2+xdydx=m2y

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Solution

y=(x+x21)m

Differentiating w.r.t x

dydx=m(x+x21)m1[1+1×2x2x21]
=m(x+x21)m1[x+x21x21]
dydx=m(x+x21)mx21
x21dydx=m(x+x21)m
=my ……….(i)

again differentiating w.r.t x

1(2x)2x21dydx+x21d2ydx2=mdydx
xdydx+(x21)d2ydx2=mx21dydx

=m(my) [From (i)]

(x21)d2ydx2+xdydx=m2y.

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