Some students find Math a very hard subject so here on BoardStudy, we have shared class 12 Math Chapter 9 Differential Equations notes. We have covered every topic in a simple and easy way so anyone can understand the chapter and perform well in exam.
Notes are very clean and colourful written by BoardStudy subject matter experts. Every important concept, formula, diagram and derivation is shared in Differential Equations notes that will help you solve the problem. These notes are designed to make complex topics easier which will definitely boost the students’ confidence during the exam.
Differential Equations Notes PDF
Chapter 8: Application of Integrals
Chapter 10: Vector Algebra Notes
Other Subjects:
Class 12 Physics Notes PDF
Class 12 Chemistry Notes PDF
Key Points
Differential Equations :An equation involving derivatives of the dependent Variable with respect to independent variable (variables) is known as a differential equation.
Order of differential equation: It is the higher order derivative occuring in the differential equation.
Degree of a differential equation: The highest exponent of the highest order derivative is called the degree of a differential equation provided differential equation should be polynomial in derivative.
NOTE: Polynomial consist of variables and coefficients and involves only addition, multiplication, substraction and non negative integral exponent.
Orders and degree (if defined) of a differential equations are always positive integers. given differential equation is not a polynomial equation in its derivatives then its degree is not defined.
Solution of differential equation: A function which satisfies the given differential equation is called its solution.
The solution which contains as many arbitrary constants as the order of the differential equation is called a general solution.
The solution free from arbitrary constants is called particular solution.
Formation of a differential equation whose general solution is given
To form differential equation from a given equation in x, y and containing arbitrary constants, the given equation is differentiated w.r.t x successively as many times as there are arbitrary constants.
These equations are used to eliminate the arbitrary constants. Thus equation obtained is required differential equation.
n general if the equation between two variables contain n arbitrary constants, then the differential equation, obtained by eliminating arbitrary constants, will of order n.
Features of Differential Equations Notes
- Differential Equations Notes are crafted by BoardStudy expert. All concepts and diagrams are included in notes.
- Our revision notes make a complex topic very simple. By using our notes, students can quickly revise Differential Equations chapter.
- In the last few days of exam, students feel very stressed due to the pressure of exam. Differential Equations Notes will be very helpful for managing the stress in the last days of the exam.
Summary
| Chapter | Differential Equations |
| Chapter Number | 9 |
| Subject | Math |
| Class | 12 |
| Medium | English |
