NCERT Solutions for Class 12 Maths Chapter 9 Differential Equations

 

NCERT Solutions for Class 12 Maths Chapter 9 Differential Equations

In class 11th we already learn how to differentiate a given function (f) with respect to an independent variable. In chapter-9 differential equations, we are going to learn some basic concepts related to differential equation, particular and general solutions of a differential equation, to solve the first order - first degree differential equation we learn some methods for this,  also learn formation of differential equations, and discuss some applications of differential equations in different areas. In this chapter, there are 6 exercises with 95 questions. The NCERT Solutions for Class 12 Maths Chapter 9 Differential Equations are solved and explained by our maths experts.

NCERT Class 12 Maths Chapter 9 Differential Equations is a very important chapter for the students,  from the 12th board exam point of view as well as competitive exams like JEE Main, because differential equations hold good weightage in the competitive exams. So, what is basically a differential equation? A differential equation is an equation in which derivatives of the dependent variable with respect to independent variables involved. Let's understand it with an example from NCERT chapter 9 Differential equations-

                                                           \\x^2-3x+3=0\;\:\:\:\:\:\:\:\:\:\:\:\:.....(1)\\ Sin\:x+cos\:x=0\:\:\:\:\:\:\:\:\:\:\:\:....(2)\\x\:+\:y\:=0\;\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:....(3)\\x\frac{dy}{dx}+y=0\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:.....(4)

From the above equations, we notice that equations (1), (2) and (3) involve dependent variable(variables) and/or independent only but equation (4) involves variables as well as derivative of the dependent variable (y) with respect to the independent variable (x)That type of equation is known as the differential equation.

Important terms used in Class 12 Chapter 9 Differential Equations-

  • Order of a differential equation-  It is the order of the highest order derivative present in the equation.
  • Degree of a differential equation-  It the power of the highest order derivative in the differential equation.
  • Homogeneous differential equation- A differential equation which can be expressed in the form \frac{dy}{dx}=f(x,\:y) where f(x,\:y) is a homogeneous function of degree zero.
  • First order linear differential equation-  A differential equation of the form \dpi{80} \frac{dy}{dx}\:+\:Py=Q where P and Q are constants or functions of x only.

Topics of NCERT Grade 12 Maths Chapter-1  Relations and Functions

9.1 Introduction

9.2 Basic Concepts

9.2.1. Order of a differential equation

9.2.2 Degree of a differential equation

9.3. General and Particular Solutions of a Differential Equation

9.4 Formation of a Differential Equation whose General Solution is given

9.4.1 Procedure to form a differential equation that will represent a given family of curves

9.5. Methods of Solving First Order, First Degree Differential Equations

9.5.1 Differential equations with variables separable

9.5.2 Homogeneous differential equations

9.5.3 Linear differential equations

NCERT Solutions for Class 12 Maths Chapter 9 Differential Equations- Solved Exercise Questions

NCERT Solutions for Class 12 Maths Chapter 9 Differential Equations Exercise 9.1

NCERT Solutions for Class 12 Maths Chapter 9 Differential Equations Exercise 9.2

NCERT Solutions for Class 12 Maths Chapter 9 Differential Equations Exercise 9.3

NCERT Solutions for Class 12 Maths Chapter 9 Differential Equations Exercise 9.4

NCERT Solutions for Class 12 Maths Chapter 9 Differential Equations Exercise 9.5

NCERT Solutions for Class 12 Maths Chapter 9 Differential Equations Exercise 9.6

NCERT Solutions for Class 12 Maths Chapter 9 Differential Equations Miscellaneous

NCERT Solutions for class 12- Maths

Chapter 1

Relations and Functions

Chapter 2

Inverse Trigonometric Functions

Chapter 3

Matrices

Chapter 4

Determinants

Chapter 5

Continuity and Differentiability

Chapter 6

Application of Derivatives

Chapter 7

Integrals

Chapter 8

Application of Integrals

Chapter 10

Vector Algebra

Chapter 11

Three Dimensional Geometry

Chapter 12

Linear Programming

Chapter 13

Probability

NCERT Solutions for Class 12

 

Boost Your Preparation with these Knockout courses

 

Recently Asked Questions

 

Related Articles

Exams
Articles
Questions