NCERT Solutions for Class 12 Maths Chapter 9 Exercise 9.5 Differential Equations - PDF Download

1. Linear differential equations

A differential equation of the from $\frac{d y}{d x}+\mathrm{P} y=\mathrm{Q}$

where, P and Q are constants or functions of x only, is known as a first order linear

differential equation. For example- $\frac{d y}{d x}+y=\sin x$

Another form of first order linear differential equation is $\frac{d x}{d y}+\mathrm{P}_1 x=\mathrm{Q}_1$ . where, P1 and Q1 are constants or functions of y only. For example- $\frac{d x}{d y}+x=\cos y$

Here are steps involved to solve the first order linear differential equation.

(i) Write the given differential equation in the form $\frac{d y}{d x}+\mathrm{P} y=\mathrm{Q}$ where P, Q are constants or functions of x only. 

(ii) Find the integrating factor$($ I.F $)=e^{\int \mathrm{P} d x}$

(iii) Write the solution of the given differential equation as

             $y(\mathrm{I} . \mathrm{F})=\int(\mathrm{Q} \times \mathrm{I} . \mathrm{F}) d x+\mathrm{C}$

Tips for Solving Exercise 9.5 Class 12 Chapter 9 Differential Equations

Our subject experts of eSaral have provided here some helpful tips and tricks for solving questions of ex 9.5 class 12 maths chapter 9.

1. By solving exercise 9.5 in NCERT solutions, you will experience different aspects of concepts as the exercise contains a variety of questions.

2. Solving questions of ex 9.5 class 12 maths will help you understand the pattern of questions asked in exams.

3. Students must learn and remember the steps of solving linear differential equations to avoid errors in exams.
   

Importance of Solving Ex 9.5 Class 12 Maths Chapter 9 Differential Equations

There are many benefits of solving ex 9.5 class 12 maths chapter 9 Differential Equations. Some of them are explained below.

1. NCERT solutions for class 12 maths chapter 9 ex 9.5 helps you to provide a deep understanding of concepts.

2. By solving questions in NCERT solutions for ex 9.5 class 12 maths will give you stepwise solutions for each question.

3. Practicing questions and revising the topic of ex 9.5 ensures the in-depth understanding of concepts.

4. You can also score high marks in exams by solving questions in NCERT solutions.

5. The answers provided in NCERT solution PDF are accurate and according to latest CBSE syllabus that will help you for preparing for board exams. 

Frequently Asked Questions

Question 1. What is a first order linear differential equation?

Answer 1. A differential equation of the form dydx+Py=Q, where P and Q are constants or functions of x only is called a first order linear differential equation.

Question 2. How many questions are there in exercise 9.5 class 12 maths chapter 9?

Answer 2. There are a total of 19 questions in ex 9.5 class 12 maths chapter 9.