y^(2)=(x-c)^(3)

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

Find the integrating factor for solving the differential equation: x(dy)/(dx)-2y=c^(2)x^(3)

Find the coordinates that the straight lines y=m_(1)x+c_(1),y=m_(2)x+c_(2) and y=m_(2)x+c_(3) may meet in a point.

If =|(2a,x_(1),y_(1)),(2b,x_(2),y_(2)),(2c,x_(3),y_(3))|=abc/2 ne 0 then the area area of the triangle whose vertices are (x_(1)/a,y_(1)/a),(x_(2)/b,y_(2)/b),(x_(3)/c,y_(3)/c) is:

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 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)

x^(2)dx-y^(2)dy+xdx=dy-ydy-dx A) 2(x^(3)-y^(3))-3(x^(2)+y^(2))+6(x-y)=c B) 2(x^(3)-y^(3))+3(x^(2)-y^(2))+6(x+y)=c C) 2(x^(3)-y^(3))-3(x^(2)+y^(2))-6(x-y)=c D) 2(x^(3)-y^(3))+3(x^(2)+y^(2))+6(x-y)=c