NCERT Solutions For Class 12 Mathematics Chapter 9: Differential Equations

Education Journalist | Study Abroad Lead

The NCERT Solutions for class 12 mathematics chapter 9 Differential Equations are given in the article. Differential equation means the derivatives of a mathematical equation. The chapter Differential Equations belongs to the unit Calculus, that adds up to 35 marks of the total marks.

Chapter 9 of NCERT Solutions for Class 12 Maths covers the concepts of order and degree of differential equations, the method of solving a differential equation, their properties and much more.

Download: NCERT Solutions for Class 12 Mathematics Chapter 9 pdf

Class 12 Maths NCERT Solutions Chapter 9 Differential Equations

NCERT Solutions

Important Topics in Class 12 Mathematics Chapter 8 Applications of Integrals

Important concepts of Class 12 Maths covered in Chapter 9 Differential Equations of NCERT Solutions are:

Order of a differential equation

The order of a differential equation is defined to be of the highest order derivative it contains. Degree of a differential equation is defined as the power to which the highest order derivative is raised.

The equation (f‴)² + (f″)⁴ + f = x is an example of a second-degree, third-order differential equation.

How to Find Order of the Differential Equation?

The order of differential equation can be found by identifying the derivatives in the given expression of the differential equation. The different derivatives in a differential equation are as follows:

First Derivative:dy/dx or y'
Second Derivative: d²y/dx², or y''
Third Derivative: d³y/dx³, or y'''
nth derivative: dny/dxn, or y''''.....n times

Further, the highest derivative present in the differential equation defines the order of the differential equation, and the exponent of the highest derivative represents the degree of the differential equation.

Formation of a Differential Equation whose General Solution is given

For any given differential equation, the solution is of the form f(x,y,a¹,a², …….,an) = 0 where x and y are the variables and a¹ , a² ……. an are the arbitrary constants.

Methods of Solving First Order, First Degree Differential Equations

Different methods of solving first order, first degree differential equations are as follows:

Differential equations with variables separable
Homogeneous differential equations
Linear differential equations

Exercise Solutions of Class 12 Maths Chapter 9 Differential Equations

Also check Exercise Solutions of Class 12 Maths Chapter 9 Differential Equations

Also Read:

Related Articles
Differential Equations Applications	Applications of Derivatives	Partial Differential Equation
Ordinary differential equations	Differential Equations Formula	Differential Calculus
Partial Derivative	Homogeneous Functions	Homogeneous Differential Equation

Check-Out:

PCMB Study Guides
NCERT Solutions for Class 12 Physics	Class 12 Physics Notes	Formulas in Physics
Topics for Comparison in Physics	Choice-based questions in physics	Topics in relation to physics
Physics Study Notes	Class 12 Physics Book PDF	Class 12 Physics Practicals
Important Derivations in Physics	SI units in Physics	Important Physics Constants and Units
Class 12 Physics Syllabus	Mendeleev's Periodic Table	NCERT Solutions for Class 12 Biology
NCERT Solutions for Class 12 English	NCERT Solutions for Class 11 Chemistry	Class 12 Chemistry Practicals
Class 12 Chemistry Notes	Important Chemical Reactions	Class 12 Maths Notes
Class 12 PCMB Notes	NCERT Class 12 Biology Book	NCERT Class 12 Maths Book
NCERT Class 12 Textbooks	NCERT Solutions for Class 11 Maths	NCERT Solutions for Class 11 Physics
NCERT Solutions for Class 12 Maths	NCERT Solutions for Class 11 Biology	NCERT Solutions for Class 11 English
NCERT Class 11 Chemistry Book	NCERT Class 11 Physics Book	NCERT Class 11 Biology Book
Class 11 Notes	Important Maths Formulas	Important Chemistry Formulas
Class 11 PCMB Syllabus	Chemistry Study Notes	Biology Study Notes
Periodic Table in Chemistry	Important Chemical Reactions	Comparison topics in Chemistry
Comparison Topics in Maths	Biology MCQs	Important Named Reactions
Maths MCQs	Comparison Topics in Biology	Chemistry MCQs

CBSE CLASS XII Related Questions

1.
Find the differential of \( x^{\cot x} + \frac{2x^2-3}{2x^2-x+2} \) with respect to \( x \).
View Solution
2.
Solve the differential equation \( (x - \sin y) \, dy + \tan y \, dx = 0 \).
View Solution
3.
A die is rolled. Consider events : \( A = \{1, 2, 5\} \), \( B = \{3, 5\} \), \( C = \{2, 3, 4, 5\} \). Find \( P(A \cap B|C) \) and \( P(A \cup B|C) \).
View Solution
4.
Evaluate : \( \int_0^2 \frac{1}{\sqrt{x^2 + 2x + 3}} \, dx \).
View Solution
5.
Three students A, B and C go to a book-store to buy art books, story books and puzzle solving books. A buys one of each type of book for a total of RS 21. B buys 4 art books, 3 story books and 2 puzzle solving books for RS 60. C buys 6 art books, 2 story books and 3 puzzle solving books and pays RS 10 more than B. Use matrix method to find the cost of each type of book.
View Solution
6.
The volume of a wooden block in the shape of a cube increases at a constant rate as the air becomes moist during the rainy season. Show that the rate of change of its surface area varies inversely as the length of edge of the cube.
View Solution