The differential equation for the family of curves `x^2+y^2-2ay=0`, where `a` is an arbitrary constant is (A) `(x^2-y^2)y\'=2xy` (B) `2(x^2+y^2)y\'=xy` (C) `2(x^2-y^2)y\'=xy` (D) `(x^2+y^2)y\'=2xy`

For the differential equation (x^2+y^2)dx-2xy dy=0 , which of the following are true. (A) solution is x^2+y^2=cx (B) x^2-y^2=cx (C) x^2-y^2=x+c (D) y(0)=0

The differential equations of all circle touching the x-axis at orgin is (a) (y^(2)-x^(2))=2xy((dy)/(dx)) (b) (x^(2)-y^(2))(dy)/(dx)=2xy ( c ) (x^(2)-y^(2))=2xy((dy)/(dx)) (d) None of these

The equation of the tangent to the curve x^(2)-2xy+y^(2)+2x+y-6=0 at (2,2) is

Find (x+y)^(2) - (x-y)^(2) ? A. 2x^(2)y^(2) B. 4xy C. 2x^(2)+2y^(2) D. x^(2)-y^(2)+2xy

Add (2x^2+5xy+2y^2), (3x^2-2xy+5y^2) and (-2x^2+8xy+3y^2)

solve: -2 (x^(2) - y^(2) + xy) - 3 (x^(2) + y^(2) - xy)

Verify : (i) x^(3)+y^(3)=(x+y)(x^(2)-xy+y^(2)) (ii) x^(3)-y^(3)=(x-y)(x^(2)+xy+y^(2))

(x)/(x-y)-(y)/(x+y)-(2xy)/(x^(2)-y^(2))

The differential equation of all conics whose centre klies at origin, is given by (a) (3xy_(2)+x^(2)y_(3))(y-xy_(1))=3xy_(2)(y-xy_(1)-x^(2)y_(2)) (b) (3xy_(1)+x^(2)y_(2))(y_(1)-xy_(3))=3xy_(1)(y-xy_(2)-x^(2)y_(3)) ( c ) (3xy_(2)+x^(2)y_(3))(y_(1)-xy)=3xy_(1)(y-xy_(1)-x^(2)y_(2)) (d) None of these

The solution of the differential equation y(xy+2x^(2)y^(2))dx+x(xy-x^(2)y^(2))dy=0, is given by