Suppose y is a function of x that sati...

Suppose y is a function of x that satisfies `(dy)/(dx)=(sqrt(1-y^(2)))/(x^(2))` and y=0 at `x=(2)/(pi)` then `y((3)/(pi))` is equal to :

A

0

B

`(1)/(2)`

C

1

D

2

Verified by Experts

The correct Answer is:

B

`(dy)/(sqrt(1-y^(2)))=(dx)/(x^(2))`
`sin^(-1)(y)=-(1)/(x)+cimpliesc=(pi)/(2)`
`sin^(-1)(y)=-(pi)/(3)+(pi)/(2)+(pi)/(6)`
`y=(1)/(2)`

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