##### VMC VIQ Scholarship Test

ApplyRegister for Vidyamandir Intellect Quest. Get Scholarship and Cash Rewards.

Edited By Lovekush kumar saini | Updated on Jan 24, 2022 04:20 PM IST

Class 12 students spend most of their time preparing for the public exams. The right solution book is required to clarify the doubts of the students in every subject, especially mathematics. Chapters like the Differential Equations are very challenging for most of the students. The RD Sharma Class 12th Exercise 21.4 reference book is very helpful for the students to complete their homework and assignments. It also lends them a helping hand in preparing for their daily tests and public exams.

**JEE Main 2025: Sample Papers | Mock Tests | PYQs | Study Plan 100 Days**

**JEE Main 2025: Maths Formulas | Study Materials**

**JEE Main 2025: Syllabus | Preparation Guide | High Scoring Topics **

Differential equations excercise 21.4 question 1

Answer: is the solution of given function.Hint:

Just differentiate the function & then put value

Given:

is the function.

Solution:

Differentiate with respect to x

Hence the function satisfies the equation.

Also, when

Thus satisfies the initial value problem.

Differential equation exercise 21.4 question 2

Answer: is the solution of given functionHint: Differentiate the function with respect to x

Given:

is the function.

Solution:

Differentiate with respect to x

Thus, satisfies the equation.

Now , When

Thus, also satisfies the given equation.

Differential equation excercise 21.4 question 3

Answer: is the solution of given function.Hint:

Take derivative of the function and check that the solution is satisfying or not.

Given:

is the function.

Solution:

Differentiate with respect to x

Thus , satisfies the initial value problem

Now,

Thus also satisfies initial value problem

Thus also satisfies initial value problem.

Differential equations excercise 21.4 question 4

Answer: is the solution of given functionHint:

Take the differentiation of the function

Given:

is the function.

Solution:

Differentiating with respect to x

Again differentiating eq(i)

Thus, satisfies the function.

Now,

When

Now,

When

Thus both satisfies the initial value problem.

Differential equations exercise 21.4 question 5

Answer: is the solution of given functionHint:

Differentiate the function and then obtain the value and satisfy initial value of problem.

Given:

is the function.

Solution:

Differentiating on both sides with respect to x

Thus,

satisfies the equation

Thus, solves initial value problem.

Differential equations excercise 21.4 question 6

Answer: is the solution of given functionHint:

Differentiate the function and then place value of x as per given.

Given:

is the function.

Solution:

Differentiating on both sides with respect to x

Thus, satistfies the equation

.

Differential equations exercise 21.4 question 7

Answer: is the solution of given functionHint:

Differentiate the function and then substitute

Given:

is the function.

Solution:

Differentiating with respect to x

Thus satisfies the equation

Now, when

Now, when

Thus both satisfies the equation.

Differential equations excercise 21.4 question 8

Hint:

Differentiate the function

Given:

is the given function

Solution:

Differentiating with respect to x

Differentiating with respect to x

Put value (i) and (ii) in different equations

Thus,

satisfies the diffrential equation

Now,when

Now,when

Thus, satisfies the initial value problem.

Differential equation exercise 21.4 question 9

Answer: is the solution of given function

Hint:

Differentiate the function

Given:

is the function.

Solution:

Differentiate with respect to x

Differentiate (i) with respect to x

Thus, satisfies the equation

Now, when

Now, when

Thus satisfies the equation and initial problem

The topics in class 12 mathematics, chapter 21, Differential Equations, are complex when compared to the other concepts in the book. There are eleven exercises in this chapter, ex 21.1 to ex 21.11. The fourth exercise, ex 21.4, consists of concepts with various methods in which the Differential Equations can be solved. The RD Sharma Class 12 Chapter 21 Exercise 21.4 book contains solved sums for the nine questions given in this exercise.

Most of the teachers pick the questions from the RD Sharma Class 12th Exercise 21.4 while conducting tests and exams. Therefore, the students who practice with the RD Sharma Solutions tend to score more marks when compared to their classmates. Moreover, various experts in the respective fields provide the answers in these solution books and are verified to check their correctness. Therefore, the students need not worry about the accuracy of the given answers.

Students can use the Class 12 RD Sharma Chapter 21 Exercise 21.4 Solution reference material to complete their homework and assignments. The same books also help them prepare for their tests, public exams, JEE mains, and other entrance exams. One of the big advantages of using the RD Sharma books is that there is no need to pay even a single rupee in order to own this book. You can find them for free at the Career 360 website.

The sums in the Differential Equations chapter take much time to solve and to recheck the answers. This can be reduced in the presence of the RD Sharma Class 12 Solutions Differential Equations Ex 21.4. Many students have given feedback that they have improved the subject knowledge and crossed their benchmark scores effortlessly with the help of the RD Sharma Class 12th Exercise 21.4.

Make the best choice of using the RD Sharma reference materials from Day 1 of your preparation for the exams. Utilize the chance to attain this set of solution books for free and own a copy of the RD Sharma Class 12 Solutions Chapter 21 Ex 21.4 from the Career 360 website.

**RD Sharma Chapter wise Solutions**

- Chapter 1 - Relations
- Chapter 2 - Functions
- Chapter 3 - Inverse Trigonometric Functions
- Chapter 4 - Algebra of Matrices
- Chapter 5 - Determinants
- Chapter 6 - Adjoint and Inverse of a Matrix
- Chapter 7 - Solution of Simultaneous Linear Equations
- Chapter 8 - Continuity
- Chapter 9 - Differentiability
- Chapter 10 - Differentiation
- Chapter 11 - Higher Order Derivatives
- Chapter 12 - Derivative as a Rate Measurer
- Chapter 13 - Differentials, Errors and Approximations
- Chapter 14 - Mean Value Theorems
- Chapter 15 - Tangents and Normals
- Chapter 16 - Increasing and Decreasing Functions
- Chapter 17 - Maxima and Minima
- Chapter 18 - Indefinite Integrals
- Chapter 19 - Definite Integrals
- Chapter 20 - Areas of Bounded Regions
- Chapter 21 - Differential Equations
- Chapter 22 - Algebra of Vectors
- Chapter 23 - Scalar Or Dot Product
- Chapter 24 - Vector or Cross Product
- Chapter 25 - Scalar Triple Product
- Chapter 26 - Direction Cosines and Direction Ratios
- Chapter 27 - Straight Line in Space
- Chapter 28 - The Plane
- Chapter 29 - Linear programming
- Chapter 30- Probability
- Chapter 31 - Mean and Variance of a Random Variable

1. What is so special about the RD Sharma solutions books?

The RD Sharma books are the most recommended set of solution materials among the students and the teachers.

2. The questions for the public exams are also picked from the practice questions section given in this book.

How many sums are solved in the RD Sharma solution guide for Exercise 21.4 given in the textbook?

There are around nine questions present in Exercise 21.4 given in the class 12 mathematics textbook. You can find the solved sums for all these questions in the RD Sharma Class 12th Exercise 21.4 book.

3. Can the students use the RD Sharma books to prepare for their public exams?

The students can refer to this best set of solution books for their public exam preparations, JEE mains, and other entrance exam preparations.

4. What is the best source to download the RD Sharma Solutions book?

The Career 360 website is the best source to download the RD Sharma solution books as it gives access to everyone for free of cost.

5. Which reference guide would help the students to solve the sums in the Differential Equations chapter with ease?

The RD Sharma Class 12th Exercise 21.4 reference book consists of many possible methods to solve the sums. Therefore, this is the best option for the students to clarify their doubts in Differential equation sums.

Sep 17, 2024

Application Date:05 September,2024 - 20 September,2024

Application Date:05 September,2024 - 23 September,2024

Admit Card Date:13 September,2024 - 07 October,2024

Admit Card Date:13 September,2024 - 07 October,2024

Get answers from students and experts

Register for Vidyamandir Intellect Quest. Get Scholarship and Cash Rewards.

Register for Tallentex '25 - One of The Biggest Talent Encouragement Exam

As per latest 2024 syllabus. Physics formulas, equations, & laws of class 11 & 12th chapters

As per latest 2024 syllabus. Chemistry formulas, equations, & laws of class 11 & 12th chapters

Accepted by more than 11,000 universities in over 150 countries worldwide

Register now for PTE & Unlock 10% OFF : Use promo code: 'C360SPL10'. Limited Period Offer! Trusted by 3,500+ universities globally

News and Notifications

Back to top