##### VMC VIQ Scholarship Test

ApplyRegister for Vidyamandir Intellect Quest. Get Scholarship and Cash Rewards.

Edited By Ramraj Saini | Updated on Apr 23, 2022 12:59 PM IST

**Introduction:** Differential equation belongs to the 9 chapter of NCERT. The NCERT Class 12 Maths chapter 9 notes is based on the differential equation. Class 12 Maths chapter 9 notes have important formulas and their derivations. A Class 12 Maths chapter 9 notes help a student to get detailed information about differential equations. Notes for Class 12 Maths chapter 9 is made in the sequence which is starting from the order of equation, degree of the equation to the types of the differential equation like a method of variable separation, homogeneous differential equation, and linear differential equation. NCERT Notes for Class 12 Maths chapter 9 not only covers the NCERT portion but also cover the CBSE class 12 maths chapter 9 notes portion.

After going through Class 12 differential equation notes students can also refer to,

**Also read :**

- NCERT Solutions for Class 12 Maths Chapter 9 Differential Equations
- NCERT Exemplar Class 12 Maths Chapter 9 Solutions Differential Equations

The basic definition of a differential equation is it is such a kind of equation that involves a derivation of a function or functions.

For a given function g, find the function of f such that

The above-given equation is called a differential equation.

An example of a general differential equation is

is an ordinary Differential equation

General notation

Order of the Differential equation

The order one differential equation is defined by the equation dy/dx = x. Here, the given function cannot be differentiated more than one time. So, it is called the first-order derivative. The same goes for equation (2).

Its order is 1

Its order is 2

Degree of a Differential equation

It is defined as the highest order derivative it contains. In other words, it is the power to which the highest order derivative is raised.

Let us see an example

It has a degree of 1 because the power of the highest order is 1

Example:

Find the order and degree of the given equation

Solution:

The order of the equation is 2 and the degree of the equation is 1

General and Particular Solution of a Differential equation

Let us consider a curve y=f(x)=asin (x+b) where a, b R and

Here the function consists of 2 arbitrary constants a and b and they are known as general solutions of a differential equation. And is the function does not contain any arbitrary constant is called a particular solution.

Formation of a Differential equation whose general solution is given

We know that

Represents a circle with centre at (-1,2) and a radius of 1

On differentiating it we get

This is a differential equation that represents a family of circles.

Now in the equation y=mx+c by giving different values to parameters m and c, we get different members of the family of a straight line.

Procedure to form a differential equation

a) If the family of curves F depends on one parameter then it is represented by

F(x, y, a) =0

On differentiating it we get

F(x, y, y’)=0

b) If the family of curves F depends on a two-parameter then it is represented by

F(x, y, a, b)

On differentiating it we get

F(x, y, y’, y’’)=0

Methods of solving first order, first-degree Differential equation

Here we will find 3 ways of solving the differential equation

Method of variable separation

Method of homogeneous differential equation

Method of Linear differential equation

Differential equation with variable separation

Firstly first order, first-degree equation is

Now if F(x, y) is expressed as g(x) h(y) then

Now separating variables we can write as

Now integrating

This gives the result as

H(y)=G(x)+c

Now let us see some examples

Homogeneous Differential equation

Let us consider a function

Now if we replace x and y with αx and αy, for any non-zero constant we get

Now in the case of differential equation

A differential equation of the form dy /dx = F (x, y) is said to be homogenous if F(x, y) is a homogenous function of zero degrees. Solving a homogeneous differential equation of the type

dy/dx = F(x, y) = g(y/x) ----------(1)

We make substitution y = v.x ------(2)

Differentiating (2) with respect to x we get

Therefore (6) gives the solution f (1) when we replace v by y/x

Let us see an example

Linear Differential Equation

If an equation is

Where P and Q are constants of x and the equation is called linear differential Equation

Steps for solving linear differential equation

First, give the equation to a general form, i.e.

Find the integrating factor(I.F.) which is equal to

Then write the equation in the following format

Let us see an example

From here we come to the end of the chapter.

Class 12 differential equation notes are helpful for the revision of the detailed chapter and for getting a glimpse of the important topics covered in the notes. Class 12 Math chapter 9 Notes is useful for getting a glance at the Class 12 CBSE Syllabus and also for national competitive exams. Class 12 Maths chapter 9 notes pdf download can be used for getting a hard copy and to prepare for the exam.

differential equation Class 12 notes pdf download: link

- NCERT Exemplar Class 12 Solutions
- NCERT Exemplar Class 12 Maths
- NCERT Exemplar Class 12 Physics
- NCERT Exemplar Class 12 Chemistry
- NCERT Exemplar Class 12 Biology

JEE Main Highest Scoring Chapters & Topics

Just Study 40% Syllabus and Score upto 100%

Download EBook- NCERT Solutions for Class 12 Mathematics
- NCERT Solutions for Class 12 Chemistry
- NCERT Solutions for Class 12 Physics
- NCERT Solutions for Class 12 Biology

1. Define Differential Equation?

In NCERT Class 12 Maths chapter 9 a differential equation is an equation with one or more derivatives of a function. The differential of the function is given by dy/dx.

2. How many types of differential equations are there and what are they?

Six types of differential equations are there

(i) Ordinary Differential Equations

(ii) Partial Differential Equations

(iii)Homogeneous Differential Equations

(iv)Non-homogeneous Differential Equations

(v) Linear Differential Equations

(vi)Nonlinear Differential Equations

3. Define the order of the differential Equation?

Order is the highest order derivative present in the differential equation is called the order of the equation. If the order is 1, then it is called the first order. If the order is 2, then it is called a second-order, and so on.

4. Uses of a differential equation-

The main purpose of the differential equation is to evaluate the function over its entire domain. It is used to describe exponential decay or growth over time. It has the capability to predict the world around us. It’s widely used in various fields like Physics, Chemistry, Biology, Economics, and many more.

5. What textbook should be followed?

Class 12 Maths chapter 9 notes and textbook should be followed.

6. From where we can download these notes?

The notes can be downloaded from differential equation Class 12 notes pdf download

Application Date:09 September,2024 - 14 November,2024

Application Date:09 September,2024 - 14 November,2024

Admit Card Date:13 September,2024 - 07 October,2024

Admit Card Date:13 September,2024 - 07 October,2024

Get answers from students and experts

Register for Vidyamandir Intellect Quest. Get Scholarship and Cash Rewards.

Register for Tallentex '25 - One of The Biggest Talent Encouragement Exam

As per latest 2024 syllabus. Physics formulas, equations, & laws of class 11 & 12th chapters

As per latest 2024 syllabus. Chemistry formulas, equations, & laws of class 11 & 12th chapters

Accepted by more than 11,000 universities in over 150 countries worldwide

Register now for PTE & Unlock 20% OFF : Use promo code: 'C360SPL20'. Limited Period Offer! Trusted by 3,500+ universities globally

News and Notifications

Back to top