The solution of the equation `(x^2y+x^2)dx+y^2(x-1)dy=0` is given by (a) `( b ) (c) (d) x^(( e )2( f ))( g )+( h ) y^(( i )2( j ))( k )+2(( l ) (m) x-y (n))+21n (o)(( p )(( q ) (r) x-1( s ))(( t ) (u) y+1( v )))/( w ) c (x) (y)=0( z )` (aa) (bb) `( c c ) (dd) (ee) x^(( f f )2( g g ))( h h )+( i i ) y^(( j j )2( k k ))( l l )+2(( m m ) (nn) x-y (oo))+1n (pp)(( q q )(( r r ) (ss) x-1( t t ))(( u u ) (vv) y+1( w w )))/( x x ) c (yy) (zz)=0( a a a )` (bbb) (ccc) `( d d d ) (eee) (fff) x^(( g g g )2( h h h ))( i i i )+( j j j ) y^(( k k k )2( l l l ))( m m m )+2(( n n n ) (ooo) x-y (ppp))-21n (qqq)(( r r r )(( s s s ) (ttt) x-1( u u u ))(( v v v ) (www) y+1( x x x )))/( y y y ) c (zzz) (aaaa)=0( b b b b )` (cccc) (dddd) None of these

Options

A. `x^(2)+y^(2)+2(x-y)+2"ln"((x-1)(y+1))/(c)=0`
B. `x^(2)+y^(2)+2(x-y)+"ln"((x-1)(y+1))/(c)=0`
C. `x^(2)+y^(2)+2(x-y)-2"ln"((x-1)(y+1))/(c)=0`
D. None of these

Answer

A

Explanation

`x^(2)(y+1)dx+y^(2)(x-1)dy=0`
or `(x^(2)dx)/(x-1)=-(y^(2)dy)/(y+1)`
or `int[x+1+1/x-1]dx=-int[y-1+1/(y+1)]`dy
or `x^(2)/2+x+" ln" (x-1)=[y^(2)/2-y"ln "(y+1)]+"ln "c`
or `(x^(2)+y^(2))/2+(x+y)+"ln "((x-1)(y+1))/c=0`