Which of the following is not the differential equation of family of curves whose tangent form an angle of `pi/4` with (a) `( b ) (c) (d)(( e ) dy)/( f )(( g ) dx)( h ) (i)=( j )(( k ) x-y)/( l )(( m ) x+y)( n ) (o) (p)` (q) (b) `( r ) (s) (t)(( u ) dy)/( v )(( w ) dx)( x ) (y)=( z ) x/( a a )(( b b ) x-y)( c c ) (dd) (ee)` (ff) (c) `( d ) (e) (f)(( g ) dy)/( h )(( i ) dx)( j ) (k)=( l )(( m ) x+y)/( n )(( o ) y-x)( p ) (q) (r)` (s) (d) None of these

Options

A. `(dy)/(dx)=(x-y)/(x+y)`
B. `(dy)/(dx) = x/(x-y)`
C. `(dy)/(dx) = (x+y)/(y-x)`
D. None of these

Answer

B

Explanation

`xy=C`
or `x(dy)/(dx)+y=0`
or `(dy)/(dx)=-y/x=m_(1)`
By condition,
`tanpi/4=|(m_(1)-m_(2))/(1+m_(1)m_(2))|`
`1=|(-y/x-m_(2))/(1-y/xm_(2))|`
or `y/x+m_(2)=1-y/xm_(2)` or `y/xm_(2)-1`
or `(dy)/(dx) = (x-y)/(x+y)` or `(dy)/(dx) = (x+y)/(y-x)`