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General

Easy

Question

The differential equation $y fraction numerator d y over denominator d x end fraction plus x equals o$ ( $0$ is any constant) represents

A set of circles having centre on the $y$ ‐axis
A set of circles centre on the $x$ ‐axis
A set of ellipses
None of these Ans

hint Hint:

We are given a differential equation. We have to solve the equation to find what it represents.

The correct answer is: A set of circles centre on the $x$ ‐axis

The given equation is $y fraction numerator d y over denominator d x end fraction plus space x space equals space o$
Here "o" is any constant.
We will solve the differential equation by variable seperation method. In this method, we take one variable on one side and other on other side. Then we integrate both the sides to find the solution.
$y fraction numerator d y over denominator d x end fraction plus x space equals space o S u b t r a c t i n g space x space f r o m space b o t h space t h e space s i d e s space w e space g e t comma y fraction numerator d y over denominator d x end fraction space equals space o space minus space x M u l t i p l y i n g space b o t h space t h e space s i d e s space b y space d x y d y space equals space left parenthesis o space minus space x right parenthesis d x I n t e g r a t i n g space b o t h space t h e space s i d e s integral y space d y space equals space integral left parenthesis o space minus space x right parenthesis d x space space fraction numerator space space space y squared over denominator 2 space end fraction space equals space o x space minus x squared over 2 R e a r r a g i n g space t h e space t e r m s y squared over 2 plus space x squared over 2 space equals space o x M u l t i p l y i n g space b o t h space s i d e s space 2 y squared space plus space x squared space equals space 2 o x$
This is the equation of set of circles having their center on x-axis.

For such questions, we know different methods to solve differential equations. We should also know the formulas of different shapes.

An integrating factor of the differential equation $x fraction numerator d y over denominator d x end fraction plus y to the power of 1 end exponent o g x equals x e to the power of x end exponent x to the power of negative fraction numerator 1 over denominator 2 end fraction 1 o g x end exponent comma$ $left parenthesis x greater than 0 right parenthesis$ is

Maths-General

General

Maths-

The solution of the differential equation $fraction numerator d y over denominator d x end fraction plus fraction numerator 3 x to the power of 2 end exponent over denominator 1 plus x to the power of 3 end exponent end fraction y equals fraction numerator s i n to the power of 2 end exponent x over denominator 1 plus x to the power of 3 end exponent end fraction$ is

For such questions, we should know different methods to solve differential equation.

The solution of the differential equation $fraction numerator d y over denominator d x end fraction plus fraction numerator 3 x to the power of 2 end exponent over denominator 1 plus x to the power of 3 end exponent end fraction y equals fraction numerator s i n to the power of 2 end exponent x over denominator 1 plus x to the power of 3 end exponent end fraction$ is

Maths-General

For such questions, we should know different methods to solve differential equation.

General

Maths-

The solution of $left parenthesis x minus y to the power of 3 end exponent right parenthesis d x plus 3 x y to the power of 2 end exponent d y equals 0$ is

Maths-General

General

Maths-

$y equals fraction numerator x over denominator x plus 1 end fraction$ is a solution of the differential equation —.

For such questions, we should know different method to solve differential equation.

$y equals fraction numerator x over denominator x plus 1 end fraction$ is a solution of the differential equation —.

Maths-General

For such questions, we should know different method to solve differential equation.

General

Maths-

The degree of the differential equation $y left parenthesis x right parenthesis equals 1 plus fraction numerator d y over denominator d x end fraction plus fraction numerator 1 over denominator 1.2 end fraction left parenthesis fraction numerator d y over denominator d x end fraction right parenthesis to the power of 2 end exponent plus fraction numerator 1 over denominator 1.2.3 end fraction left parenthesis fraction numerator d y over denominator d x end fraction right parenthesis to the power of 3 end exponent plus$ is

For such questions, we should know the definition of power.

The degree of the differential equation $y left parenthesis x right parenthesis equals 1 plus fraction numerator d y over denominator d x end fraction plus fraction numerator 1 over denominator 1.2 end fraction left parenthesis fraction numerator d y over denominator d x end fraction right parenthesis to the power of 2 end exponent plus fraction numerator 1 over denominator 1.2.3 end fraction left parenthesis fraction numerator d y over denominator d x end fraction right parenthesis to the power of 3 end exponent plus$ is

Maths-General

For such questions, we should know the definition of power.

General

Maths-

If $left parenthesis fraction numerator 2 plus blank s i n blank x over denominator 1 plus y end fraction right parenthesis fraction numerator d y over denominator d x end fraction equals negative blank c o s blank x comma$ $y left parenthesis 0 right parenthesis equals 1$ , then $y left parenthesis fraction numerator pi over denominator 2 end fraction right parenthesis equals$

Maths-General

General

Maths-

The differential equation $fraction numerator d to the power of 2 end exponent y over denominator 2 end fraction plus x fraction numerator d y over denominator d x end fraction plus blank s i n blank y plus x to the power of 2 end exponent equals 0$ is of the $d x$ following type

Maths-General

General

Maths-

The point of intersection of tangents at the ends of the latus rectum of the parabola $y to the power of 2 end exponent equals 4 x text is equal to end text$

Maths-General

General

Maths-

The equation of family of curves for which the length of the normal is equal to the radius vector is

Maths-General

General

Maths-

The general solution of $y to the power of 2 end exponent d x plus left parenthesis x to the power of 2 end exponent minus x y plus y to the power of 2 end exponent right parenthesis d y equals 0$ is

Maths-General

General

Maths-

The curve satisfying $y equals 2 x fraction numerator d y over denominator d x end fraction$ is a

Maths-General

General

Maths-

The differential equation of the family of curves $c y to the power of 2 end exponent equals 2 x plus c comma$ where $c$ is an arbitrary constant is

Maths-General

General

Maths-

$text The line end text x minus y plus 2 equals 0 text touches the parabola end text y to the power of 2 end exponent equals 8 x text at the end text$ point

Maths-General

General

Maths-

The solution of the differential equation $fraction numerator d y over denominator d x end fraction equals fraction numerator y over denominator x end fraction plus fraction numerator f comma left parenthesis fraction numerator y over denominator x end fraction right parenthesis over denominator empty set left parenthesis fraction numerator y over denominator x end fraction right parenthesis end fraction$ is

Maths-General

General

Maths-

Solution of $fraction numerator x d y over denominator x to the power of 2 end exponent plus y to the power of 2 end exponent end fraction equals left parenthesis fraction numerator y over denominator x to the power of 2 end exponent plus y to the power of 2 end exponent end fraction 1 right parenthesis d x$ is

Maths-General

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The differential equation $y fraction numerator d y over denominator d x end fraction plus x equals o$ ( $0$ is any constant) represents

A set of circles having centre on the $y$ ‐axis
A set of circles centre on the $x$ ‐axis
A set of ellipses
None of these Ans

We are given a differential equation. We have to solve the equation to find what it represents.

The correct answer is: A set of circles centre on the $x$ ‐axis

Related Questions to study

The solution of $left parenthesis x minus y to the power of 3 end exponent right parenthesis d x plus 3 x y to the power of 2 end exponent d y equals 0$ is

The solution of $left parenthesis x minus y to the power of 3 end exponent right parenthesis d x plus 3 x y to the power of 2 end exponent d y equals 0$ is

$y equals fraction numerator x over denominator x plus 1 end fraction$ is a solution of the differential equation —.

$y equals fraction numerator x over denominator x plus 1 end fraction$ is a solution of the differential equation —.

The differential equation $fraction numerator d to the power of 2 end exponent y over denominator 2 end fraction plus x fraction numerator d y over denominator d x end fraction plus blank s i n blank y plus x to the power of 2 end exponent equals 0$ is of the $d x$ following type

The differential equation $fraction numerator d to the power of 2 end exponent y over denominator 2 end fraction plus x fraction numerator d y over denominator d x end fraction plus blank s i n blank y plus x to the power of 2 end exponent equals 0$ is of the $d x$ following type

The point of intersection of tangents at the ends of the latus rectum of the parabola $y to the power of 2 end exponent equals 4 x text is equal to end text$

The point of intersection of tangents at the ends of the latus rectum of the parabola $y to the power of 2 end exponent equals 4 x text is equal to end text$

The equation of family of curves for which the length of the normal is equal to the radius vector is

The equation of family of curves for which the length of the normal is equal to the radius vector is

The general solution of $y to the power of 2 end exponent d x plus left parenthesis x to the power of 2 end exponent minus x y plus y to the power of 2 end exponent right parenthesis d y equals 0$ is

The general solution of $y to the power of 2 end exponent d x plus left parenthesis x to the power of 2 end exponent minus x y plus y to the power of 2 end exponent right parenthesis d y equals 0$ is

The curve satisfying $y equals 2 x fraction numerator d y over denominator d x end fraction$ is a

The curve satisfying $y equals 2 x fraction numerator d y over denominator d x end fraction$ is a

The differential equation of the family of curves $c y to the power of 2 end exponent equals 2 x plus c comma$ where $c$ is an arbitrary constant is

The differential equation of the family of curves $c y to the power of 2 end exponent equals 2 x plus c comma$ where $c$ is an arbitrary constant is

$text The line end text x minus y plus 2 equals 0 text touches the parabola end text y to the power of 2 end exponent equals 8 x text at the end text$ point

$text The line end text x minus y plus 2 equals 0 text touches the parabola end text y to the power of 2 end exponent equals 8 x text at the end text$ point

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Can’t find what you’re looking for?

The differential equation ( is any constant) represents

A set of circles having centre on the ‐axis A set of circles centre on the ‐axis A set of ellipses None of these Ans

We are given a differential equation. We have to solve the equation to find what it represents.

The correct answer is: A set of circles centre on the ‐axis

Related Questions to study

An integrating factor of the differential equation is

An integrating factor of the differential equation is

The solution of the differential equation is

The solution of the differential equation is

The solution of is

The solution of is

is a solution of the differential equation —.

is a solution of the differential equation —.

The degree of the differential equation is

The degree of the differential equation is

If , then

If , then

The differential equation is of the following type

The differential equation is of the following type

The point of intersection of tangents at the ends of the latus rectum of the parabola

The point of intersection of tangents at the ends of the latus rectum of the parabola

The equation of family of curves for which the length of the normal is equal to the radius vector is

The equation of family of curves for which the length of the normal is equal to the radius vector is

The general solution of is

The general solution of is

The curve satisfying is a

The curve satisfying is a

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

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

point

point

The solution of the differential equation is

The solution of the differential equation is

Solution of is

Solution of is

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The differential equation $y fraction numerator d y over denominator d x end fraction plus x equals o$ ( $0$ is any constant) represents

A set of circles having centre on the $y$ ‐axis
A set of circles centre on the $x$ ‐axis
A set of ellipses
None of these Ans

The correct answer is: A set of circles centre on the $x$ ‐axis

The solution of $left parenthesis x minus y to the power of 3 end exponent right parenthesis d x plus 3 x y to the power of 2 end exponent d y equals 0$ is

The solution of $left parenthesis x minus y to the power of 3 end exponent right parenthesis d x plus 3 x y to the power of 2 end exponent d y equals 0$ is

$y equals fraction numerator x over denominator x plus 1 end fraction$ is a solution of the differential equation —.

$y equals fraction numerator x over denominator x plus 1 end fraction$ is a solution of the differential equation —.

The differential equation $fraction numerator d to the power of 2 end exponent y over denominator 2 end fraction plus x fraction numerator d y over denominator d x end fraction plus blank s i n blank y plus x to the power of 2 end exponent equals 0$ is of the $d x$ following type

The differential equation $fraction numerator d to the power of 2 end exponent y over denominator 2 end fraction plus x fraction numerator d y over denominator d x end fraction plus blank s i n blank y plus x to the power of 2 end exponent equals 0$ is of the $d x$ following type

The point of intersection of tangents at the ends of the latus rectum of the parabola $y to the power of 2 end exponent equals 4 x text is equal to end text$

The point of intersection of tangents at the ends of the latus rectum of the parabola $y to the power of 2 end exponent equals 4 x text is equal to end text$

The general solution of $y to the power of 2 end exponent d x plus left parenthesis x to the power of 2 end exponent minus x y plus y to the power of 2 end exponent right parenthesis d y equals 0$ is

The general solution of $y to the power of 2 end exponent d x plus left parenthesis x to the power of 2 end exponent minus x y plus y to the power of 2 end exponent right parenthesis d y equals 0$ is

The curve satisfying $y equals 2 x fraction numerator d y over denominator d x end fraction$ is a

The curve satisfying $y equals 2 x fraction numerator d y over denominator d x end fraction$ is a

The differential equation of the family of curves $c y to the power of 2 end exponent equals 2 x plus c comma$ where $c$ is an arbitrary constant is

The differential equation of the family of curves $c y to the power of 2 end exponent equals 2 x plus c comma$ where $c$ is an arbitrary constant is

$text The line end text x minus y plus 2 equals 0 text touches the parabola end text y to the power of 2 end exponent equals 8 x text at the end text$ point

$text The line end text x minus y plus 2 equals 0 text touches the parabola end text y to the power of 2 end exponent equals 8 x text at the end text$ point