A curve passing through `(2,3)` and satisfying the differential equation `int_0^x ty(t)dt=x^2y(x),(x >0)` is (a) `( b ) (c) (d) x^(( e )2( f ))( g )+( h ) y^(( i )2( j ))( k )=13 (l)` (m) (b) `( n ) (o) (p) y^(( q )2( r ))( s )=( t )9/( u )2( v ) (w) x (x)` (y) (c) `( d ) (e) (f)(( g ) (h) x^(( i )2( j ))( k ))/( l )8( m ) (n)+( o )(( p ) (q) y^(( r )2( s ))( t ))/( u )(( v ) 18)( w ) (x)=1( y )` (z) (d) `( a a ) (bb) x y=6( c c )` (dd)

Options

A. `x^(2)+y^(2)=13`
B. `y^(2)=9/2x`
C. `x^(2)/8+y^(2)/18=1`
D. `xy=6`

Answer

D

Explanation

`int_(0)^(t)ty(dt) = x^(2)y(x)`
Differentiating w.r.t. x we get
`xy(x) = x^(2)y^(')(x)+2xy(x)`
or `xy(x)+x^(2)y^(')(x)=0`
or `x(dy)/(dx)=y=0`
or `logy+logx=logc`
or `xy=c`