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## NCERT Class 12 Maths Textbook Chapter 9 With Answer PDF Free Download

### Chapter 4: Differential Equations

#### 9.1 Introduction

In Class XI and in Chapter 5 of the present book, we discussed how to differentiate a given function f with respect to an independent variable, i.e., how to find f ′(x) for a given function f at each x in its domain of definition.

Further, in the chapter on Integral Calculus, we discussed how to find a function f whose derivative is the function g, which may also be formulated as follows:

For a given function g, find a function f such that dy/dx = g(x), where y = f(x) … (1)

An equation of the form (1) is known as a differential equation. A formal definition will be given later.

These equations arise in a variety of applications, may it be in Physics, Chemistry, Biology, Anthropology, Geology, Economics, etc.

Hence, an in-depth study of differential equations has assumed prime importance in all modern scientific investigations.

In this chapter, we will study some basic concepts related to differential equations, general and particular solutions of a differential equation,

formation of differential equations, some methods to solve a first-order – first-degree differential equation, and some applications of differential equations in different areas.

Author | NCERT |

Language | English |

No. of Pages | 45 |

PDF Size | 699 KB |

Category | Mathematics |

Source/Credits | ncert.nic.in |

### NCERT Solutions Class 12 Maths Chapter 9 Differential Equations

Question 1:

Determine order and degree(if defined) of differential equation

ANSWER:

The highest order derivative present in the differential equation is. Therefore, its order is four.

The given differential equation is not a polynomial equation in its derivatives. Hence, its degree is not defined

Question 2:

Determine order and degree(if defined) of differential equation

ANSWER:

The given differential equation is:

The highest order derivative present in the differential equation is. Therefore, its order is one.

It is a polynomial equation in. The highest power raised tois 1. Hence, its degree is one.

Question 3:

Determine order and degree(if defined) of differential equation

ANSWER:

The highest order derivative present in the given differential equation is. Therefore, its order is two.

It is a polynomial equation inand. The power raised tois 1.

Hence, its degree is one.

Question 4:

Determine order and degree(if defined) of differential equation

ANSWER:

The highest order derivative present in the given differential equation is. Therefore, its order is 2.

The given differential equation is not a polynomial equation in its derivatives. Hence, its degree is not defined.

Question 5:

Determine order and degree(if defined) of differential equation

ANSWER:

The highest order derivative present in the differential equation is. Therefore, its order is two.

It is a polynomial equation inand the power raised tois 1.

Hence, its degree is one.

NCERT Class 12 Maths Textbook Chapter 9 With Answer PDF Free Download