The differential equation of all circle of radius r, is given by
(a) `{1+(y_(1))^(2)}^(2)=r^(2)y_(2)^(3)`
(b) `{1+(y_(1))^(2)}^(3)=r^(2)y_(2)^(3)`
( c ) `{1+(y_(1))^(2)}^(3)=r^(2)y_(2)^(2)`
(d) None of these

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

Show the differential equation : x + y = tan^(-1)y : y^(2)y' + y^(2) + 1 = 0

The differential equation satisfying the curve (x^(2))/(a^(2)+lambda)+(y^(2))/(b^(2)+lambda)=1 where lambda be arbitary uknown, 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

If y=(tan^(-1)x)^(2) show that (x^(2)+1)^(2)y_(2)+2x(x^(2)+1)y_(1)=2

The equation of the circle having radius 3 and touching the circle x^(2) + y^(2)-4x -6y - 12 = 0 at (-1,-1) is

If y=(tan^(-1)x)^(2) , show that (x^(2)+1)^(2)y_(2)+2x(x^(2)+1)y_(1)=2 .

If x = 2/t^(2), y = t^(3)-1, (d^(2)y)/(dx^(2) ) =

The degree of the differential equation (d^(2)y)/(dx^(2)) + [1+ (dy/dx)^(2)]^(3/2) = 0

The order and degree of the differential equation : [ 1 + ( (d y) / (d x) ) ^5 ] ^(1 / 3) = (d ^2 y) / (d x^ 2)

If m and n are order and degree of the differential equation ((d^(2)y)/(dx^(2)))^(5) + (((d^(2)y)/(dx^(2)))^(3)) /(((d^(3)y)/(dx^(3))) ) + (d^(3)y)/(dx^(3)) = x^(2)-1 then