### Differential equations of Circles

Differential Equation (XV) Formation of Differential Equations by Elimination Find the differential equations of all circles of radius (whatever their radii or positions in the plane xOy).

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Differential Equation (XV) Formation of Differential Equations by Elimination Find the differential equations of all circles of radius (whatever their radii or positions in the plane xOy).

Differential Equation (XII) Formation of Differential Equations by Elimination Find the differential equations of all parabolas whose axes are parallel to the axis of y.

Differential Equation (IX): Formation of Differential Equations by Elimination Eliminate the arbitrary constants from the equation: y = Ae^x + Be^2x + Ce^3x. Make sure to show all of the steps which are involved.

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A seismograph is a scientific instrument that is used to detect earthquakes. A simple model of a seismograph is shown below. It consists of a particle of mass m to which a pointer is attached. The particle is suspended by a spring of natural length lo and stiffness k and a damper of damping constant r from a platform of height d

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