Question

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

Answer 1

Correct Answer - b
` (dy)/(dx) (xlog x) +y = 2 log x`
` rArr (dy)/(dx) +y/(x log x ) = 2/x`
Here , ` P = 1/(x log x ),Q = 2/x`
` :. IF = e^(intPdx) = e^(int(dx)/(x logx) )= log x `