The equation of the curve satisfying xdy−ydx=x2−y2−−−−−−√ and y(1)=0 is:

y=x2log(sinx)

y=xsin(logx)

y2=x(x−1)2

y=2x2(x−1)

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The equation of the curve satisfying xdy−ydx=x2−y2−−−−−−√ and y(1)=0 is:

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[b] The given equation can be rewritten as x2[xdy−ydxx2]=x1−y2x2−−−−−−√ ⇒x2ddx(yx)=x1−y2x2−−−−−−√ Put yx=z, we get sin−1(z)=logx+c⇒sin−1(yx)=logx+c Apply the boundary value y(1) = 0 ⇒sin−1(01)=log1+c⇒c=0 ∴sin−1(yx)=logx+0⇒y=xsin(logx)

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