The general solution of the equation `(dy)/(dx)=1+x y` is (a) `( b ) (c) y=c (d) e^( e ) (f)-( g )(( h ) (i) x^((( j )2( k ))( l ))/( m )2( n ) (o) (p))( q ) (r)` (s) (b) `( t ) (u) y=c (v) e^( w ) (x) (y)(( z ) (aa) x^((( b b )2( c c ))( d d ))/( e e )2( f f ) (gg) (hh))( i i ) (jj)` (kk) (c) `( d ) (e) y=(( f ) (g) x+c (h)),( i ) e^( j ) (k)-( l )(( m ) (n) x^((( o )2( p ))( q ))/( r )2( s ) (t) (u))( v ) (w)` (x) (d) None of these

Options

A. `y=ce^(-x^(2)//2)`
B. `y=ce^(x^(2)//2)`
C. `y=(x+c),e^(-x^(2)//2)`
D. None of these

Answer

D

Explanation

`(dy)/(dx)=1+xy`
or `(dy)/(dx)-xy=1`
I.F. `=e^(int-xdx)=e^(-x^(2)//2)`
Hence solution is `y.e^(-x^(2)//2) = inte^(-x^(2)+2)dx+c`.
`inte^(-x^(2)//2)dx` is not further integrable.