Class 12 Chapter 9: Differential Equations
A Differential Equation is an equation involving a dependent variable, an independent variable, and one or more of its derivatives. It provides a mathematical model for describing changing quantities and is widely used in physics, engineering, biology, economics, and population studies. This chapter introduces the formation, order, degree, and solution of first-order differential equations using standard methods. It is an important topic in CBSE Board, JEE Main, and JEE Advanced, combining conceptual understanding with analytical problem-solving.
At ALLEN, these revision notes simplify Differential Equations through concise theory, important formulas, standard solving techniques, solved examples, and exam-focused strategies. These notes are ideal for quick revision and building confidence for both board and competitive examinations.
1.0Chapter Snapshot
2.0Related Supporting Study Resources
3.0Learning Outcomes
After completing this chapter, you will be able to:
- Understand the concept of differential equations.
- Identify the order and degree of a differential equation.
- Form differential equations from given functions.
- Solve first-order first-degree differential equations.
- Apply the method of variable separation.
- Verify the solution of differential equations.
- Solve JEE Main, JEE Advanced, and CBSE Board questions effectively.
4.05-Minute Quick Revision
Must-Revise Concepts
- Differential Equation
- Order of Differential Equation
- Degree of Differential Equation
- Formation of Differential Equations
- General Solution
- Particular Solution
- Variable Separable Method
- Homogeneous Differential Equations
- Verification of Solutions
- Applications of Differential Equations
Important Formula Recall
- General form: F(x,y,dxdy)=0
- Variable separable form: dxdy=f(x)g(y)
- Separated form: g(y)dy=f(x),dx
Important Properties / Shortcut Tips
- Determine the order before solving the equation.
- Simplify the equation before identifying its degree.
- Check whether variables can be separated.
- Always include the constant of integration.
- Verify the obtained solution by differentiation whenever required.
5.0High Weightage Topics
6.0Formula Handbook
7.0Common Mistakes & JEE Tips
8.0ALLEN Faculty Tips
- Strengthen your integration concepts before studying this chapter.
- Memorize the definitions of order and degree thoroughly.
- Practice variable separable equations regularly.
- Solve formation-based questions to improve conceptual understanding.
- Verify your answers whenever possible.
- Practice Previous Years' Questions (PYQs) for better speed and accuracy.
9.0PYQ Trend Analysis
Differential Equations is a frequently tested chapter in CBSE Board, JEE Main, and JEE Advanced. Questions generally focus on identifying order and degree, solving first-order differential equations, and applying the method of separation of variables.
Note: The trend below is based on the analysis of previous years' JEE Main and JEE Advanced question papers. The exact number of questions may vary each year.
10.0Most Common Question Types
- Finding the order and degree of a differential equation.
- Forming differential equations from given functions.
- Solving variable separable differential equations.
- Finding general and particular solutions.
- Verifying whether a given function satisfies a differential equation.
- Applying integration techniques to solve differential equations.
- Solving concept-based and previous years' examination questions.
11.0Smart Revision Strategy
- Revise integration formulas before starting this chapter.
- Learn the concepts of order and degree thoroughly.
- Practice formation of differential equations.
- Solve variable separable equations.
- Revise general and particular solutions.
- Verify solved equations to improve accuracy.
- Practice Previous Years' Questions (PYQs).
- Complete revision with a timed chapter test.