The differential equation satisfying the curve `(x^(2))/(a^(2)+lambda)+(y^(2))/(b^(2)+lambda)=1` when `lambda` begin arbitary uknowm, is
(a) `(x+yy_(1))(xy_(1)-y)=(a^(2)-b^(2))y_(1)`
(b) `(x+yy_(1))(xy_(1)-y)=y_(1)`
( c ) `(x-yy_(1))(xy_(1)+y)(a^(2)-b^(2))y_(1)`
(d) None of these

The degree of the differential equation satisfying the relation sqrt(1+x^2) + sqrt(1+y^2) = lambda (x sqrt(1+y^2)- ysqrt(1+x^2)) is

Solve the differential equation (dy)/(dx)=(x+2y-1)/(x+2y+1).

The differential equation of all conics whose centre lies 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 differential equation which represents the family of curves y=c_(1)e^(c_(2^(x) where c_(1)andc_(2) are arbitary constants is

If the curves ax^(2)+by^(2)=1 and a'x^(2)+b'y^(2)=1 are orthogonally then …………

The differential equation of all straight lines which are at a constant distance p from the origin, is (a) (y+xy_1)^(2)=p^(2) (1+y_(1)^2) (b) (y-xy_(1)^(2))=p^(2) (1+y_(1))^(2) ( c ) (y-xy_(1))^(2)=p^(2) (1+y_(1)^(2)) (d) None of these

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 differential equation of all circle in the first quadrant touch the coordinate is (a) (x-y)^(2)(1+y')^(2)=(x+yy')^(2) (b) (x-y)^(2)(1+y')^(2)=(x+y')^(2) ( c ) (x-y)^(2)(1+y')=(x+yy')^(2) (d) None of these

The differential equation having y=(sin^(-1)x)^(2)+A(cos^(-1)x)+B , where A and B are abitary constant , is

(1 + x^(2))(dy)/(dx) + 2xy = (1)/(1 + x^(2)), y = 0 when x= 1