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Question

If ey+xy=e, the ordered pair (dydx,d2ydx2) at x=0 is equal to :

A
(1e,1e2)
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B
(1e,1e2)
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C
(1e,1e2)
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D
(1e,1e2)
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Solution

The correct option is A (1e,1e2)
Given equation, ey+xy=e,
As x=0y=1
ey dydx+xdydx+y=0 (1)
dydx=yey+x
At x=0, y=1dydx=1e
On differentiating (1) again, we have -
ey (dydx)2+ey d2ydx2+xd2ydx2+2dydx=0

At x=0, y=1
e(1e)2+ed2ydx22e=0

ed2ydx2=1e

d2ydx2=1e2

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