The solution of differential equation `(2y+x y^3)dx+(x+x^2y^2)dy=0` is (a) `( b ) (c) (d) x^(( e )2( f ))( g ) y+( h )(( i ) (j) x^(( k )3( l ))( m ) (n) y^(( o )3( p ))( q ))/( r )3( s ) (t)=c (u)` (v) (b) `( w ) (x) x (y) y^(( z )2( a a ))( b b )+( c c )(( d d ) (ee) x^(( f f )3( g g ))( h h ) (ii) y^(( j j )3( k k ))( l l ))/( m m )3( n n ) (oo)=c (pp)` (qq) (c) `( d ) (e) (f) x^(( g )2( h ))( i ) y+( j )(( k ) (l) x^(( m )4( n ))( o ) (p) y^(( q )4( r ))( s ))/( t )4( u ) (v)=c (w)` (x) (d) None of these

Options

A. `x^(2)y+(x^(3)y^(3))/3=c`
B. `xy^(2)+(x^(3)y^(3))/3=c`
C. `x^(2)y+(x^(4)y^(4))/4=c`
D. None of these

Answer

A

Explanation

`(2y+xy^(3))dx+(x+x^(2)y^(2))dy=0`
or `(2ydx+xdy)+(xy^(3)dx+x^(3)y^(2)dy)=0`
or `d(x^(2)y)+1/3d(x^(3)y^(3))=0`
Integrating, we get `x^(2)y+(x^(3)y^(3))/3+c`