Formation of Differential Equation
Formation of Differential Equation: Overview
This topic covers concepts, such as, Formation of Differential Equations by Eliminating Arbitrary Constants & Formation of Differential Equation Representing a Given Family of Curves etc.
Important Questions on Formation of Differential Equation
The differential equation corresponding to the family of curves given by where and are arbitrary constants is

The differential equation of the family of circles with fixed radius units and centre on the line , is

The order and the degree of the differential equation of all ellipses with centre at the origin, major axis along -axis and eccentricity are, respectively

The differential equation satisfied by the family of curves given by is...
where are arbitrary constant

The differential equation of all parabolas each of which has a latus rectum 4a and whose axes are parallel to the Y-axis is

The differential equation of all straight lines passing through the origin is

Differential equation of all family of lines by eliminating the arbitrary constant is

The family of curves , where is an arbitrary constant, is represented by the differential equation

Form the differential equation representing the family of curves , where are arbitrary constant.

The differential equation by eliminating the arbitrary constants from the following equation: will be

If , then is equal to

Form the differential equation of all parabolas whose axis is axis.

Form the differential equation of all parabolas having the vertex at origin and axis along the positive axis.

Form the differential equation of the family of circles touching the axis at the origin.

Find the differential equation of the family of circles having their centres on the line and touching theaxis.

A particle is moving along the axis. Its acceleration at time is proportional to its velocity at that time. Find the differential equation of the motion of the particle.

Obtain the differential equation by eliminating the arbitrary constants from the following equation.

Obtain the differential equation by eliminating the arbitrary constants from the following equation.

Obtain the differential equation by eliminating the arbitrary constants from the following equation.

Obtain the differential equation by eliminating the arbitrary constants:
