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

Options

A. `y="ln" (x)+C`
B. `y^(2)=("ln "x)^(2)+c`
C. `y=logx+xy`
D. `xy=x^(y)+c`

Answer

B

Explanation

The given equation is reduced to `x=e^(xy(dy//dx))`
or `logx=xy(dy)/(dx)`
or `intydy=int1/xlogxdx`
or `y^(2)/2=(logx)^(2)/2+C`