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Question

The differential equation satisfied by the curves e2y+2bxey+b2=0, where b is a parameter, is

A
(1+x2)d2ydx2=0
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B
(x21)(dydx)21=0
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C
(x21)d2ydx2+2=0
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D
(x2x)dydxy2=0
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Solution

The correct option is B (x21)(dydx)21=0
e2y+2bxey+b2=0
e2y+2bxey+b2x2=b2x2b2
(ey+bx)2=b2(x21)
ey+bx=±bx21
ey=b(x±x21) (1)

Differentiating equation (1) with respect to x, we get
eydydx=b(x21±x)x21 (2)

From equations (1) and (2),
x21dydx=±1
(x21)(dydx)2=1

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