" (iv) "y^(2)=(x+c)^(3)

Equation of the parabola with focus (0,-3) and the directrix y=3 is: (a) x^(2)=-12y (b) x^(2)=12y (c) x^(2)=3y (d) x^(2)=-3y

The solution of ((dy)/(dx))^(2)+(2x+y)(dy)/(dx)+2xy=0, is (i) (y+x^(2)-c_(1))(x+log y+y^(2)+c_(2))( (ii) (y+x^(2)-c_(1))(x-log y-c_(2))( iii) (y+x^(2)-c_(1))(x+log y-c_(2))( iv) (y+x^(2)-c_(1))(3x+log y-c_(2))

Form the differential equation of the family of curves represented c(y+c)^(2)=x^(3) where c is a parameter.

The general solution of the differential equation x^2(1+y^3)dx=y^2(1+x^3)dy is (A) (1+x^2)(1+y^2)=C (B) 1+x^3=C(1+y^3) (C) (x+y)(1+x^2+x^3)=C (D) x(1+y^2)=Cy(1+x^2)

The general solution of the differential equation x^2(1+y^3)dx=y^2(1+x^3)dy is (A) (1+x^2)(1+y^2)=C (B) 1+x^3=C(1+y^3) (C) (x+y)(1+x^2+x^3)=C (D) x(1+y^2)=Cy(1+x^2)

The value of the determinant |[x,x+y, x+2y], [x+2y, x,x+y], [x+y, x+2y,x]| is (a) 9x^2(x+y) (b) 9y^2(x+y) (c) 3y^2(x+y) (d) 7x^2(x+y)

The value of the determinant |[x, x+y, x+2y], [x+2y, x,x+y],[x+y, x+2y, x]| is (a) 9x^2(x+y) (b) 9y^2(x+y) (c) 3y^2(x+y) (d) 7x^2(x+y)

From the differential equation of the family of curves represented by y^2 = (x-c)^3