Let x=x(y) be the solution of the differential equation y= (x-y ~d x ~d y ) ( x y ), y 0 and x(1)= 2 . Then (x(2)) is equal to :

Step-by-step solution

aligned & y d y=(x d y-y d x) ( x y ) & d y y = ( x d y-y d x y^2 ) ( x y ) & d y y = ( x y ) d (- x y ) & n y= x y +C aligned aligned & x(1)= 2 0= 2 +C C=0 & lny = x y & but y=2 x 2 = n 2 & x=2 ^2 x 2 -1 & =2( 2)^2-1 aligned