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Question

If y is a function of x and log(x+y)2xy=0 then the value of y(0) is equal to

A
1
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B
1
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C
2
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D
0
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Solution

The correct option is A 1
When x=0, we have
log(0+y)2×0×y=0
logy=0
y=e0=1
Given equation is
log(x+y)2xy=0
On differentiating w,r,t x we get
1x+y(1+dydx)2y2xdydx=0
On putting x=0,y=1 we get
(1+dydx)20=0
(1+dydx)2=0
dydx=1
ie,y(x)=1
y(0)=1

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