The solution of `(x^2+x y)dy=(x^2+y^2)dx` is (a) `( b ) (c)logx=log(( d ) (e) x-y (f))+( g ) y/( h ) x (i) (j)+c (k)` (l) (m) `( n ) (o)logx=2log(( p ) (q) x-y (r))+( s ) y/( t ) x (u) (v)+c (w)` (x) (y) `( z ) (aa)logx=log(( b b ) (cc) x-y (dd))+( e e ) x/( f f ) y (gg) (hh)+c (ii)` (jj) (kk) None of these

The equation of a curve passing through (1,0) for which the product of the abscissa of a point P and the intercept made by a normal at P on the x-axis equal twice the square of the radius vector of the point P is (a) ( b ) (c) (d) x^(( e )2( f ))( g )+( h ) y^(( i )2( j ))( k )=( l ) x^(( m )4( n ))( o ) (p) (q) (b) ( r ) (s) (t) x^(( u )2( v ))( w )+( x ) y^(( y )2( z ))( a a )=2( b b ) x^(( c c )4( d d ))( e e ) (ff) (gg) (c) ( d ) (e) (f) x^(( g )2( h ))( i )+( j ) y^(( k )2( l ))( m )=4( n ) x^(( o )4( p ))( q ) (r) (s) (d) None of these

x log x(dy)/(dx) + y = (2)/(x)log x

The circumcenter of the triangle formed by the line y=x ,y=2x , and y=3x+4 is (a) ( b ) (c)(( d ) (e)6,8( f ))( g ) (h) (b) ( i ) (j)(( k ) (l)6,8( m ))( n ) (o) (c) ( d ) (e)(( f ) (g)3,4( h ))( i ) (j) (d) ( k ) (l)(( m ) (n)-3,-4( o ))( p ) (q)

A curve is such that the mid-point of the portion of the tangent intercepted between the point where the tangent is drawn and the point where the tangent meets the y-axis lies on the line y=xdot If the curve passes through (1,0), then the curve is (a) ( b ) (c)2y=( d ) x^(( e )2( f ))( g )-x (h) (i) (b) ( j ) (k) y=( l ) x^(( m )2( n ))( o )-x (p) (q) (c) ( d ) (e) y=x-( f ) x^(( g )2( h ))( i ) (j) (k) (d) ( l ) (m) y=2(( n ) (o) x-( p ) x^(( q )2( r ))( s ) (t))( u ) (v)

x(dy)/(dx)+2y-x^(2)logx=0

If u = log ((x ^(2) y + y ^(2) x)/(xy)) then x (del u)/( del x) + y (del u)/(del y)=

If y = (e^(x) + logx + 1)^(50) find (dy)/(dx) .

The general solution of x((dy)/(dx))+(logx)y=x^(-1/2logx) is