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A function y=f(x) satisfies (x+1)f^(prim...

A function `y=f(x)` satisfies `(x+1)f^(prime)(x)-2(x^2+x)f(x)=(e^x^2)/((x+1)),AAx >-1.` If `f(0)=5,` then `f(x)` is (a) `( b ) (c)(( d ) (e) (f)(( g )3x+5)/( h )(( i ) x+1)( j ) (k) (l))( m ) e^( n ) (o) (p) x^((( q )2( r ))( s ) (t))( u ) (v)` (w) (b) `( x ) (y)(( z ) (aa) (bb)(( c c )6x+5)/( d d )(( e e ) x+1)( f f ) (gg) (hh))( i i ) e^( j j ) (kk) (ll) x^((( m m )2( n n ))( o o ) (pp))( q q ) (rr)` (ss) (c) `( d ) (e)(( f ) (g) (h)(( i )6x+5)/( j )(( k ) x+1)( l ) (m) (n))( o ) e^( p ) (q) (r) x^((( s )2( t ))( u ) (v))( w ) (x)` (y) (d) `( z ) (aa)(( b b ) (cc) (dd)(( e e )5-6x)/( f f )(( g g ) x+1)( h h ) (ii) (jj))( k k ) e^( l l ) (mm) (nn) x^((( o o )2( p p ))( q q ) (rr))( s s ) (tt)` (uu)

A

`((3x+5)/(x+1)).e ^(x ^(2))`

B

`((6x+5)/(x+1)).e ^(x ^(2))`

C

`((6x+5)/(x+1)^(2)).e ^(x ^(2))`

D

`((5x+6x)/(x+1)).e ^(x ^(2))`

Text Solution

Verified by Experts

The correct Answer is:
B
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