An equation of the curve satisfying xdy−ydx=√x2−y2 dx and y(1)=0 is
A
y=x2log|sinx|
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B
y=xsin(log|x|)
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C
y2=x(x−1)2
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D
y=2x2(x−1)
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Solution
The correct option is By=xsin(log|x|) The equation can be written as x2xdy−ydxx2=x√1−(yx)2dx ⇒d(yx)√1−(yx)2=dxx⇒Sin−1yx=log|x|+const. Since y(1) = 0 so const = 0. Hence y = x sin (log |x|)