NCERT Solutions for Class 12 Maths Chapter 9 Exercise 9.3 Differential Equations - PDF Download

1. Methods of Solving First Order, First Degree Differential Equations

In this part, you will get to know three methods of solving first order first degree differential equations. In exercise 9.3, we will discuss the first method which is differential equations with variables separable.

• Differential equations with variables separable

As we know a first order-first degree differential equation is of the form

            $\frac{d y}{d x}=\mathrm{F}(x, y)$       …..(1)

If F (x, y) can be expressed as a product g(x) h(y), where, g(x) is a function of x and h(y) is a function of y, then the differential equation (1) is said to be of variable separable type. The differential equation (1) then has the form

                  $\frac{d y}{d x}=h(y) \cdot g(x)$             ….(2)

If h(y) ≠ 0, separating the variables, (2) can be rewritten as

                  $\frac{1}{h(y)} d y=g(x) d x$                ….(3)

Integrating both sides of (3), we get

            $\int \frac{1}{h(y)} d y=\int g(x) d x$    ….(4)

Thus, (4) provides the solutions of given differential equation in the form

                          H(y) = G(x) + C

Here, H (y) and G (x) are the antiderivatives of 1h(y) and g (x) respectively and C is the arbitrary constant. 

Tips for Solving Exercise 9.3 Class 12 Chapter 9 Differential Equations

NCERT solutions for class 12 maths chapter 9 ex 9.3 has questions based on different methods of solving first order-first degree differential equations. Here, our subject matter experts have combined useful and helpful tips for solving exercise 9.3 class 12 maths chapter 9.

1. Students should have a good command on differential equations with variables separable to understand the process of solving questions.

2. It is very important that you read the question carefully as some of the questions are word problems.

3. Students should also remember the formula of differential equations for different methods to understand the concept of each question.
   

Importance of Solving Ex 9.3 Class 12 Maths Chapter 9 Differential Equations

Solving questions of ex 9.3 class 12 maths chapter 9 will give you a lot of benefits. eSaral’s expert teachers of mathematics have provided here some of them which you can check below.

1. eSaral’s experienced faculties have encompassed the method of solving first order, first degree differential equations with variables separable that ensures the in-depth understanding of this topic. 

2.  Questions in ex 9.3 class 12 maths ch 9 are solved with step by step method to help you comprehend the concepts.

3. NCERT solutions for ex 9.3 class 12 maths are also available here in PDF format that have included answers in simple and precise language for students that will help you in board exams.

4. These solutions not only provide answers to exercise questions but also include all the concepts related to exercise so that you can solve all the questions without being confused.

Frequently Asked Questions

Question 1. What do you understand about the variable separable method?

Answer 1. Variable separable method is used to solve such an equation in which variables can be separated completely i.e. terms containing y should remain with dy and terms containing x should remain with dx.

Question 2. Is it important to solve all the questions of exercise 9.3 class 12 maths chapter 9?

Answer 2. Yes, it is very important to solve each question of exercise 9.3 class 12 maths chapter 9. Ex 9.3 class 12 maths has questions based on the topic of differential equations by variable separable method, students must comprehend the concept to solve the questions. Every question has a different nature of itself so it is essential for you to solve all the questions. You can also download the NCERT solution PDF from eSaral website to practice these questions.