Solution of the differential equation `{1/x-(y^2)/((x-y)^2)}dx+{(x^2)/((x-y)^2)-1/y}dy=0` is (a) `( b ) (c)1n|( d ) (e) x/( f ) y (g) (h)|+( i )(( j ) dy)/( k )(( l ) x-y)( m ) (n)=c (o)` (p) (b) `( q ) (r) (s)(( t ) x y)/( u )(( v ) x-y)( w ) (x)=c (y) e^(( z ) (aa) (bb) x/( c c ) y (dd) (ee) (ff))( g g ) (hh)` (ii) (c) `( d ) (e)1n|( f ) x y|=c+( g )(( h ) x y)/( i )(( j ) x-y)( k ) (l) (m)` (n) (d) None of these

Options

A. `"ln"|x/y|+(xy)/(x-y)=c`
B. `(xy)/(x-y)=ce^(x//y)`
C. `"ln"|xy|+(x^(4)y^(4))/4=C`
D. None of these

Answer

A

Explanation

`{1/x-y^(2)/(x-y)^(2)}dx+{x^(2)/(x-y)^(2)-1/y}dy=0`
or `((dx)/x-(dy)/y)+((x^(2)dy-y^(2)dx))/((x-y)^(2))=0`
or `((dx)/x-(dy)/y)+((dy//y^(2)-dx//x^(2))/((1//y-1//x)^(2)))=0`
Integrating, we get `"ln "|x|-"ln "|y|-1/(1//x-1//y)=c`
or `"ln "|x/y|+(xy)/(x-y)=c`