Let y(x) be a solution of `xdy+ydx+y^(2)(xdy-ydx)=0` satisfying y(1)=1. Statement -1 : The range of y(x) has exactly two points. Statement-2 : The constant of integration is zero.A. Statement-1 is True, Statement-2 is True, Statement-2 is a correct explanation for Statement-1.B. Statement-1 is True, Statement-2 is True, Statement-2 is not a correct explanation for Statement-1.C. Statement-1 is True, Statement-2 is False.D. Statement-1 is False, Statement-2 is True.

Let y(x) be a solution of `xdy+ydx+y^(2)(xdy-ydx)=0` satisfying y(1)=1

1.	Let y(x) be a solution of `xdy+ydx+y^(2)(xdy-ydx)=0` satisfying y(1)=1. Statement -1 : The range of y(x) has exactly two points. Statement-2 : The constant of integration is zero.A. Statement-1 is True, Statement-2 is True, Statement-2 is a correct explanation for Statement-1.B. Statement-1 is True, Statement-2 is True, Statement-2 is not a correct explanation for Statement-1.C. Statement-1 is True, Statement-2 is False.D. Statement-1 is False, Statement-2 is True.
Answer» Correct Answer - C We have, `xdy+ydx+y^(2)(xdy-ydx)=0` `rArr" "d(xy)+x^(2)y^(2){(xdy-ydx)/(x^(2))}=0` `rArr" "(1)/((xy)^(2))d(xy)+d((y)/(x))=0` On integrating, we get `-(1)/(xy)+(y)/(x)=C" …(i)"` It is given that y = 1 when x = 1 `therefore" "-1+1=C rArr C=0` Putting C = 0 in (i), we get `-(1)/(xy)+(y)/(x)=0 rArr y^(2)-1=0 rArr y = pm1` Clearly, statement-1 and statement-2 are true. Also, statement-2 is not a correct explanation for statement-1.

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