The integrating factor of the differential equation `(dy)/(dx)(x(log)_e x)+y=2(log)_e x` is given by (a) `( b ) x (c)` (d) (b) `( e ) (f) (g) e^(( h ) x (i))( j ) (k)` (l) (c) `( m ) (n) (o)(( p )log)_( q ) e (r) (s) x (t)` (u) (d) `( v ) (w) (x)(( y )log)_( z ) e (aa) (bb)(( c c )(( d d )log)_( e e ) e (ff) (gg) x)( h h )` (ii)

Options

A. x
B. `e^(x)`
C. `log_(e)x`
D. `log_(e)(log_(e)x)`

Answer

C

Explanation

`therefore (dy)(dx)+y/(xlog_(e)x)=2/x`
`therefore` I.F. `=e^(int1/(xlog_(e)x)dx)`
`=e^(log_(e )(log_(e)x)`
`=log_(e)x`