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$The solution of the differential equation 3 {xy}^{1} - 3 y + {(x^{2} - y^{2})}^{1 / 2} = 0 satisfying the condition y(1)=1 is$

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3cos-1(y/x)=lnx

3cos(y/x)=lnx

3cos-1(y/x)=2logx

3sin-1(y/x)=lnx

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detailed solution

Correct option is A

−dydx=3y−x2−y23x, put y=vxdydx=v+xdvdx∫31−v2dv=−∫dxx⇒3cos−1⁡(y/x)=log⁡|x|+cPass_(1,1)_⇒c=03cos-1(y/x)=lnx

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The solution of the differential equation 3xy1−3y+x2−y21/2=0 satisfying the condition y(1)=1 is

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$The solution of the differential equation 3 {xy}^{1} - 3 y + {(x^{2} - y^{2})}^{1 / 2} = 0 satisfying the condition y(1)=1 is$