The differential equation of all non-horizontal lines in a plane is (a) `( b ) (c) (d)(( e ) (f) d^(( g )2( h ))( i ) y)/( j )(( k ) d (l) x^(( m )2( n ))( o ))( p ) (q) (r)` (s) (b) `( t ) (u) (v)(( w ) (x) d^(( y )2( z ))( a a ) x)/( b b )(( c c ) d (dd) y^(( e e )2( f f ))( g g ))( h h ) (ii)=0( j j )` (kk) (c) `( d ) (e) (f)(( g ) dy)/( h )(( i ) dx)( j ) (k)=0( l )` (m) (d) `( n ) (o) (p)(( q ) dx)/( r )(( s ) dy)( t ) (u)=0( v )` (w)

Options

A. `(d^(2)y)/(dx^(2))`
B. `(d^(2)x)/(dy^(2))=0`
C. `(dy)/(dx)=0`
D. `(dx)/(dy)=0`

Answer

B

Explanation

The general equation of all non-horizontal lines in xy-plane is `ax+by=1`, where `a ne 0`.
Now, `ax + by=1`
or `a(dx)/(dy)+b=0` [Differentiating w.r.t y]
or `a(d^(2)x)/(dy^(2))=0` [Differentiating w.r.t. y]
or `(d^(2)x)/(dy^(2))=0` `[therefore a ne 0]`
Hence, hte required differential equation is `(d^(2)x)/(dy^(2))=0`