The solution of differential equation `(y(2x^4+y)dy)/(dx)=(1-4x y^2)x^2` is given by (a) `( b ) (c)3( d ) (e)(( f ) (g) (h) x^(( i )2( j ))( k ) y (l))^(( m )2( n ))( o )+( p ) y^(( q )3( r ))( s )-( t ) x^(( u )3( v ))( w )=c (x)` (y) (z) `( a a ) (bb) x (cc) y^(( d d )2( e e ))( f f )+( g g )(( h h ) (ii) y^(( j j )3( k k ))( l l ))/( m m )3( n n ) (oo)-( p p )(( q q ) (rr) x^(( s s )3( t t ))( u u ))/( v v )3( w w ) (xx)+c=0( y y )` (zz) (aaa) `( b b b ) (ccc) (ddd)2/( e e e )5( f f f ) (ggg) y (hhh) x^(( i i i )5( j j j ))( k k k )+( l l l )(( m m m ) (nnn) y^(( o o o )3( p p p ))( q q q ))/( r r r )3( s s s ) (ttt)=( u u u )(( v v v ) (www) x^(( x x x )3( y y y ))( z z z ))/( a a a a )3( b b b b ) (cccc)-( d d d d )(( e e e e )4x (ffff) y^(( g g g g )3( h h h h ))( i i i i ))/( j j j j )3( k k k k ) (llll)+c (mmmm)` (nnnn) (d) None of these

Options

A. `3(x^(2)y^(2))^(2)+y^(3)-x^(3)=c`
B. `xy^(2)+y^(3)/3-x^(3)/3+c=0`
C. `2/5yx^(5)+y^(3)/3=x^(3)/3-(4xy^(3))/3+c`
D. None of these

Answer

A

Explanation

`y(2x^(4)+y)(dy)/(dx) =(1-4xy^(2))x^(2)`
or `2x^(4)ydy+y^(2)dy+4x^(3)y^(2)dx-x^(2)dx=0`
or `2x^(2)y(x^(2)dy+2xydx) +y^(2)dy-x^(2)dx=0`
or `2x^(2)yd(x^(2)y)+y^(2)dy-x^(2)dx=0`
Integrating, we get `(x^(2)y)^(2)+y^(3)/3-x^(3)/3=c`
or `3(x^(2)y)^(2)+y^(3)-x^(3)=c`