Let `y(x)` be a solution of the differential equation `(1+e^x)y^(prime)+y e^x=1.` If `y(0)=2` , then which of the following statements is (are) true? (a) `( b ) (c) y(( d ) (e)-4( f ))=0( g )` (h) (b) `( i ) (j) y(( k ) (l)-2( m ))=0( n )` (o) (c) `( d ) (e) y(( f ) x (g))( h )` (i) has a critical point in the interval `( j ) (k)(( l ) (m)-1,0( n ))( o )` (p) (q) `( r ) (s) y(( t ) x (u))( v )` (w) has no critical point in the interval `( x ) (y)(( z ) (aa)-1,0( b b ))( c c )` (dd)

Options

A. y(-4)=0
B. y(-2)=0
C. y(x) has a critical point in the interval (-1,0)
D. y(x) has no critical point in the interval (-1,0)

Answer

A, C, D