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Differential equation of the family of c...

Differential equation of the family of curves `v=A/r+B ,` where `A` and `B` are arbitrary constants, is (a) `( b ) (c) (d)(( e ) (f) d^(( g )2( h ))( i ) v)/( j )(( k ) d (l) r^(( m )2( n ))( o ))( p ) (q)+( r )1/( s ) r (t) (u) (v)(( w ) d v)/( x )(( y ) d r)( z ) (aa)=0( b b )` (cc) (b) `( d d ) (ee) (ff)(( g g ) (hh) d^(( i i )2( j j ))( k k ) v)/( l l )(( m m ) d (nn) r^(( o o )2( p p ))( q q ))( r r ) (ss)-( t t )2/( u u ) r (vv) (ww)( x x )(( y y ) d v)/( z z )(( a a a ) d r)( b b b ) (ccc)=0( d d d )` (eee) (c) `( d ) (e) (f)(( g ) (h) d^(( i )2( j ))( k ) v)/( l )(( m ) d (n) r^(( o )2( p ))( q ))( r ) (s)+( t )2/( u ) r (v) (w) (x)(( y ) d v)/( z )(( a a ) d r)( b b ) (cc)=0( d d )` (ee) (d) None of these

A

`(d^(2)v)/(dr^(2)) +(1)/(r ).(dv)/(dr)=0`

B

`(d^(2)v)/(dr^(2)) -(2)/(r ).(dv)/(dr)=0`

C

`(d^(2)v)/(dr^(2))+(2)/(r )(dv)/(dr)=0`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
C
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