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Question

If y=(x+1+x2)n, then (1+x2)d2ydx2+xdydx is

A
n2y
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B
n2y
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C
y
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D
2x2y
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Solution

The correct option is A n2y
Given, y=(x+1+x2)n
dydx=n(x+1+x2)n1(1+12(1+x2)1/2.2x)
dydx=n(x+1+x2)n1(1+x2+x)1+x2=n(x+1+x2)n1+x2

1+x2dydx=ny
or
1+x2y1=ny(y1=dydx)

On squaring, we get

(1+x2)y21=n2y2

Differentiating (1+x2)y2+xy1=n2y

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