# NCERT Class 12-Mathematics: Chapter – 9 Differential Equations Part 5 (For CBSE, ICSE, IAS, NET, NRA 2023)

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**Question 22: Fill in the blanks of the following**:

(i) Order of the differential equation representing the family of parabolas is ________ .

**Answer**:

One; is the only arbitrary constant.

**(ii)** The degree of the differential equation is ________.

**Answer**:

Two; since the degree of the highest order derivative is two.

**(iii)** The number of arbitrary constants in a particular solution of the differential equation is ________ .

**Answer**:

Zero; any particular solution of a differential equation has no arbitrary constant.

**(iv)** is a homogeneous function of degree________ .

**Answer**:

Zero

**(v)** An appropriate substitution to solve the differential equation is________.

**Answer**:

**(vi)** Integrating factor of the differential equation is ________.

**Answer**:

given differential equation can be written as and therefore

**(vii)** The general solution of the differential equation is________.

**Answer**:

from given equation, we have

**(viii)** The general solution of the differential equation

**Answer**:

and the solution is .

**(ix)** The differential equation representing the family of curves is ________ .

**Answer**:

Differentiating the given function w. r. t. *x* successively, we get

And

is the differential equation.

**(x)** when written in the form , then ________.

**Answer**:

the given equation can be written as

This is a differential equation of the type

**Question 23**:

State whether the following statements are **True** or **False**.

**(i)** Order of the differential equation representing the family of ellipses having centre at origin and foci on *x*-axis is two.

**Answer**:

True, since the equation representing the given family is has two arbitrary constants.

**(ii)** Degree of the differential equation is not defined.

**Answer**:

True, because it is not a polynomial equation in its derivatives.

**(iii)** is a differential equation of the type but it can be solved using variable separable method also.

**Answer: True**

**(iv)** is not a homogeneous function.

**Answer**:

True, because .

**(v)** is a homogeneous function of degree .

**Answer**:

True, because .

**(vi)** Integrating factor of the differential equation is

**Answer**:

**(vii)** The general solution of the differential equation is .

**Answer**:

True, because given equation can be written as

**(viii)** The general solution of the differential equation is

**Answer: False**

**(ix)** is a solution of the differential equation

**Answer**:

True,

Which satisfies the given equation.

**(x)** is a particular solution of the differential equation

**Answer: False**

Because does not satisfy the given differential equation.