The solution of the differential equation `(x^2y^2-1)dy+2xy^3dx=0` is (a) `( b ) (c)1+( d ) x^(( e )2( f ))( g ) (h) y^(( i )2( j ))( k )=c x (l)` (m) (b) `( n ) (o)1+( p ) x^(( q )2( r ))( s ) (t) y^(( u )2( v ))( w )=c y (x)` (y) (c) `( d ) (e) y=0( f )` (g) (d) `( h ) (i) y=-( j )1/( k )(( l ) (m) x^(( n )2( o ))( p ))( q ) (r) (s)` (t)

Options

A. `1+x^(2)y^(2)=cx`
B. `1+x^(2)y^(2)=cy`
C. `y=0`
D. `y=-1/x^(2)`

Answer

B

Explanation

`(x^(2)y^(2)-1)dy+2xy^(3)dx=0`
or `x^(2)y^(2)dy+2xy^(3)dx=dy`
or `x^(2)dy+2xydx=(dy)/y^(2)`
or `intd(x^(2)y)=int(dy)/(y^(2))+c`
or `x^(2)y=y^(-1)/-1+c`
or `x^(2)y^(2)=-1+cy`
i.e., `1+x^(2)y^(2)=cy`