Formation of Differential Equation

IMPORTANT

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

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IMPORTANT

The differential equation corresponding to the family of curves given by ax2+by2=1 where a and b are arbitrary constants is

MEDIUM
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The differential equation of the family of circles with fixed radius r units and centre on the line y=3, is

MEDIUM
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The order and the degree of the differential equation of all ellipses with centre at the origin, major axis along X-axis and eccentricity 32 are, respectively

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The differential equation satisfied by the family of curves given by y=axcos1x+b is...

(where a, b are arbitrary constant)

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

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

MEDIUM
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Differential equation of all family of lines y=mx+4m by eliminating the arbitrary constant m is

EASY
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The family of curves y=easinx, where a is an arbitrary constant, is represented by the differential equation

MEDIUM
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Form the differential equation representing the family of curves y=a sin(x+b), where a,b are arbitrary constant.

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The differential equation by eliminating the arbitrary constants from the following equation: y=c1e2x+c2e-2x will be

HARD
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If y=tan-1x2, then x2+12y2+2xx2+1y1 is equal to

EASY
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Form the differential equation of all parabolas whose axis is Y-axis.

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

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

HARD
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Find the differential equation of the family of circles having their centres on the line y=10 and touching the X-axis.

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

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

y2=x+c3

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

y=c1+c2xex

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

y=A coslogx+Bsinlogx

MEDIUM
IMPORTANT

Obtain the differential equation by eliminating the arbitrary constants: y=c2+cx