Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 12 - Differential Equations>Target Exercises>Q 4

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IMPORTANT

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The differential equation of the system of all circles of radius $r$ in the $X Y$ -plane is

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Important Questions on Differential Equations

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JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 12 - Differential Equations>Target Exercises>Q 5

The differential equation which is satisfied by all the curves,

y = A e^{2 x} + B e^{- x / 2},

where

A

and

B

are non-zero constants, is

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JEE Advanced

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Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 12 - Differential Equations>Target Exercises>Q 6

The differential equation satisfied by

a x^{2} + b y^{2} = 1

is

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Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 12 - Differential Equations>Target Exercises>Q 7

The differential equation of the family of general circles is

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Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 12 - Differential Equations>Target Exercises>Q 8

The differential equation of all ellipses centred at the origin is

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JEE Advanced

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Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 12 - Differential Equations>Target Exercises>Q 9

The differential equation for

y = A \cos α x + B \sin α x

where

A

and

B

are arbitrary constants, is

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JEE Advanced

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Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 12 - Differential Equations>Target Exercises>Q 10

The particular solution of

\cos y d x + (1 + 2 e^{- x}) \sin y d y = 0,

when

x = 0, y = \frac{π}{4}

is

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JEE Advanced

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Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 12 - Differential Equations>Target Exercises>Q 11

The equation of the curve for which the cartesian sub-tangent varies as the reciprocal of the square of the abscissa, is

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Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 12 - Differential Equations>Target Exercises>Q 13

The solution of

\frac{d y}{d x} = \frac{a x + g}{b y + f}

represents a circle, when