Find the differential equation of a S.H.M.

Find the differential equation of all parabolas whose axis are parallel to the x-axis.

Find the differential equation of all circles which touch the x-axis at the origin.

Find the differential equation of all circles touching the x-axis at the origin .

Find the differential equation of all non-vertical lines in a plane.

Find the differential equation of all straight lines passing through the point (0,3).

Find the differential equation of the circles which touch the x-axis at the origin.

Find the differential equation of y = Ax + (B)/(x) , where A and B are arbitrary constants .

Find the differential equation of the curves given by y=Ae^(2x)+Be^(-2x) , where A and B are parameters.

Find the differential equation of the family of circles which touch the coordinate axes in the third quadrant.

Find the differential equation of the family of circles x^(2) + y^(2) = 2ay , where a is a parameter .