NCERT Class 12 Mathematics Mathematics Part-II: Chapter 3 — DIFFERENTIAL EQUATIONS
This chapter introduces the concept of differential equations, which are equations involving derivatives of a dependent variable with respect to an independent variable. It distinguishes between ordinary differential equations (ODEs) and partial differential equations (PDEs), focusing on ODEs. The chapter defines the order of a differential equation based on the highest order derivative present. It also touches upon the historical context and wide-ranging applications of differential equations in various scientific fields like Physics, Chemistry, and Economics. Students will learn about the general and particular solutions, formation of differential equations, and methods to solve first-order, first-degree differential equations, preparing them for advanced mathematical studies and problem-solving in science and engineering.
Quick info
| Board | CBSE / NCERT |
|---|---|
| Class | Class 12 |
| Subject | Mathematics |
| Book | Mathematics Part-II |
| Chapter | Chapter 3 — DIFFERENTIAL EQUATIONS |
| Language | English |
| PDF type | NCERT Textbook |
| Session | CBSE 2026 |
| Reading time | 3 minutes |
| Word count | 565 |
Learning outcomes
- Understand the definition and significance of differential equations.
- Differentiate between ordinary and partial differential equations.
- Determine the order of a given ordinary differential equation.
- Recognize the role of differential equations in various scientific applications.
Vocabulary
| Word | Meaning |
|---|---|
| Differential Equation | An equation involving derivatives of a dependent variable with respect to an independent variable. |
| Ordinary Differential Equation (ODE) | A differential equation involving derivatives with respect to only one independent variable. |
| Partial Differential Equation (PDE) | A differential equation involving derivatives with respect to more than one independent variable. |
| Order of a differential equation | The order of the highest order derivative present in the differential equation. |
| Dependent variable | The variable whose value depends on one or more other variables. |
| Independent variable | A variable that is not dependent on other variables in a given context. |
The complete chapter text is read in the official NCERT PDF viewer below (streamed from ncert.nic.in). This page provides NCERT Help study material — summary, vocabulary, practice questions, and FAQs — not a full reproduction of the textbook.
Read chapter online
This PDF is loaded from the official NCERT website (ncert.nic.in). Use the page buttons below to read — download is disabled on NCERT Help.
Read page by page below. PDF is streamed from the official NCERT website — no download button on this page.
Practice questions
- What is the difference between an ordinary differential equation and a partial differential equation? Answer: An ODE involves derivatives with respect to only one independent variable, while a PDE involves derivatives with respect to more than one independent variable.
- Define the order of a differential equation. Answer: The order of a differential equation is the order of the highest order derivative of the dependent variable with respect to the independent variable involved in the equation.
- Give an example of an equation that is NOT a differential equation. Answer: An example is x^2 - 3x + 3 = 0, which only involves variables and no derivatives.
Practice MCQs
Q1. Which of the following is a differential equation?
Explanation: The equation dy/dx + y/x = 0 involves the derivative dy/dx, making it a differential equation.
Q2. What is the order of the differential equation y/d + dy/d?
Explanation: The highest order derivative in the equation is y/d, which is of the second order.
Q3. An equation involving derivatives with respect to more than one independent variable is called:
Explanation: Differential equations with derivatives of a function of multiple independent variables are known as partial differential equations.
Q4. The equation dy/dx = g(x) is an example of:
Explanation: This equation relates a function's derivative to the independent variable, fitting the definition of a differential equation.
Q5. Which field heavily utilizes differential equations according to the text?
Explanation: The text explicitly mentions Economics, along with Physics, Chemistry, and Biology, as fields where differential equations find application.
Frequently asked questions
What is a differential equation?
A differential equation is an equation that relates a function with its derivatives.
What is the difference between an ODE and a PDE?
An ODE involves derivatives with respect to a single independent variable, while a PDE involves derivatives with respect to multiple independent variables.
How is the order of a differential equation determined?
The order is determined by the highest order derivative present in the equation.
Why are differential equations important?
They are crucial in modeling and solving problems in various scientific and engineering disciplines.
What kind of equations were discussed before differential equations in the chapter?
The chapter first revisits algebraic equations (like x^2 – 3x + 3 = 0) and equations involving only variables (like x + y = 7) before introducing differential equations.
Related resources
Important topics
Topics covered
NCERT Class 12 Mathematics — Mathematics Part-II — Chapter 3 — DIFFERENTIAL EQUATIONS. Verified by NCERT Help Editorial Team. Reviewed on 29 Jul 2026. Last updated 10 Aug 2026.