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RD Sharma books are the gold standard for class 12 maths. They are the best material that students can refer to get in detail knowledge about the subject and get familiar with a lot of concepts. A majority of schools all over the country use RD Sharma books to set up question papers as well as to follow in their class lectures. This is why it remains the number one choice among students for maths.

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Class 12 RD Sharma chapter 21 exercise 21.1 covers the chapter Differential Equations. This exercise contains 42 questions that are of Level-1 difficulty. Students can easily get through the solutions with a basic understanding of the chapter. With the help of RD Sharma Solutions Differential Equations Ex 21.1. Students can quickly finish the exercise and save time for their revision.

Differential Equation exercise 21.1 question 1

Answer:

Hint:

The order is the highest numbered derivative in the equation with no negative or fractional power of the dependent variable and its derivatives, while the degree is the highest power to which a derivative is raised.

Given:

Solution:

So, in this question, the order of the differential equation is 3 and the degree of the differential equation is 1.

In a differential equation, when the dependent variable and their derivatives are only multiplied by constant or independent variable, then the equation is linear.

So, in this question. The dependent variable is x and the term is multiplied by itself. So the given equation is non-linear.

Therefore, Order=3 , Degree=1 , Non-linear

Differential Equation exercise 21.1 question 2

Answer:

Order=2 , Degree=1 , linearHint:

The order is the highest numbered derivative in the equation with no negative or fractional power of the dependent variable and its derivatives, while the degree is the highest power to which a derivative is raised.

Given:

Solution:

So, in this question, the order of the differential equation is 2 and the degree of the differential equation is 1.

In a differential equation, when the dependent variable and their derivatives are only multiplied by constant or independent variable, then the equation is linear.

So, in this question. The dependent variable is y and its derivatives are multiplied with a constant or independent variable only. So this equation is linear differential equation.

Therefore, Order=2 , Degree=1 , linear

Differential Equation exercise 21.1 question 3

Hint:

The order is the highest numbered derivative in the equation with no negative or fractional power of the dependent variable and its derivatives, while the degree is the highest power to which a derivative is raised.

Given:

Solution:

So, in this question, first we need to remove the term because this can be written as which means a negative power.

So, the above equation becomes

So, in this question, the order of the differential equation is 1 and the degree of the differential equation is 3.

In a differential equation, when the dependent variable and their derivatives are only multiplied by constant or independent variable, then the equation is linear.

So, in this question. The dependent variable is y and the term is multiplied by itself. So the given equation is non-linear.

Therefore, Order=1 , Degree=3 , Non-linear

Differential Equation exercise 21.1 question 4

Answer:

Order=2 , Degree=2 , Non-linearHint:

The order is the highest numbered derivative in the equation with no negative or fractional power of the dependent variable and its derivatives, while the degree is the highest power to which a derivative is raised.

Given:

Solution:

In this question, we will raising both the sides the power 6. So we remove the fractional powers of derivatives of the dependent variable y.

So, the above equation becomes

So, in this question, the order of the differential equation is 2 and the degree of the differential equation is 2.

In a differential equation, when the dependent variable and their derivatives are only multiplied by constant or independent variable, then the equation is linear.

So, in this question. The dependent variable is y and the term is multiplied by itself and many other are also. So the given equation is non-linear.

Therefore, Order=2 , Degree=2 , Non-linear

Differential Equation exercise 21.1 question 5

Answer:

Order=2 , Degree=1, Non-linearHint:

The order is the highest numbered derivative in the equation with no negative or fractional power of the dependent variable and its derivatives, while the degree is the highest power to which a derivative is raised.

Given:

Solution:

So, in this question, the order of the differential equation is 2 and the degree of the differential equation is 1.

In a differential equation, when the dependent variable and their derivatives are only multiplied by constant or independent variable, then the equation is linear.

So, in this question. The dependent variable is y and the term is multiplied by itself. So the given equation is non-linear.

Therefore, Order=2 , Degree=1 , Non-linear

Differential Equation exercise 21.1 question 6

Hint:

The order is the highest numbered derivative in the equation with no negative or fractional power of the dependent variable and its derivatives, while the degree is the highest power to which a derivative is raised.

Given:

Solution:

Squaring on both sides, we get

Cubing on both sides,

So, in this question, the order of the differential equation is 2 and the degree of the differential equation is 2.

In a differential equation, when the dependent variable and their derivatives are only multiplied by constant or independent variable, then the equation is linear.

So, in this question. The dependent variable is y and the term is multiplied by itself. So the given equation is non-linear.

Therefore, Order=2 , Degree=2 , Non-linear

Differential Equation exercise 21.1 question 7

Hint:

The order is the highest numbered derivative in the equation with no negative or fractional power of the dependent variable and its derivatives, while the degree is the highest power to which a derivative is raised.

Given:

Solution:

Since this equation has fractional powers, we need to remove them.

So squaring on both sides, we get

Solving both sides,

So, in this question, the order of the differential equation is 4 and the degree of the differential equation is 2.

In a differential equation, when the dependent variable and their derivatives are only multiplied by constant or independent variable, then the equation is linear.

So, in this question. The dependent variable is y and the term is multiplied by itself, also the degree of the

equation is 2 which must be one for the equation to be linear. So the given equation is non-linear.

Therefore, Order=4 , Degree=2 , Non-linear

Differential Equation exercise 21.1 question 8

Hint:

The order is the highest numbered derivative in the equation with no negative or fractional power of the dependent variable and its derivatives, while the degree is the highest power to which a derivative is raised.

Given:

Solution:

Since this equation has fractional powers, we need to remove them.

So squaring on both sides, we get

So, in this question, the order of the differential equation is 1 and the degree of the differential equation is 2.

In a differential equation, when the dependent variable and their derivatives are only multiplied by constant or independent variable, then the equation is linear.

So, in this question. The dependent variable is y and its derivatives are multiplied with a constant or independent variable only. So this equation is linear differential equation.

Therefore, Order=1 , Degree=2 , linear

Differential Equation exercise 21.1 question 9

Answer:

Order=2 , Degree=1, linearHint:

The order is the highest numbered derivative in the equation with no negative or fractional power of the dependent variable and its derivatives, while the degree is the highest power to which a derivative is raised.Given:

Solution:

Here in this question, the dependent variable is x and thus the order of the differential equation is 2 and the degree of the differential equation is 1.

In a differential equation, when the dependent variable and their derivatives are only multiplied by constant or independent variable, then the equation is linear.

So, in this question. The dependent variable is x and its derivatives are multiplied with a constant or independent variable only. So this equation is linear differential equation.

Therefore, Order=2 , Degree=1 , linear

Differential Equation exercise 21.1 question 10

Answer:

Order=2, Degree=1, Non- linear

Hint:

The order is the highest numbered derivative in the equation with no negative or fractional power of the dependent variable and its derivatives, while the degree is the highest power to which a derivative is raised.

Given:

_{}

Solution:

Here in this question, the dependent variable is_{ t }and thus the order of the differential equation is 2 and the degree of the differential equation is 1.

In a differential equation, when the dependent variable and their derivatives are only multiplied by constant or independent variable, then the equation is linear.

Here the dependent variable is_{ t }and its derivatives are multiplied together with_{}. So this equation is non-linear differential equation.

Therefore, Order=2, Degree=1, Non-linear

Differential Equation exercise 21.1 question 11

Hint:

The order is the highest numbered derivative in the equation with no negative or fractional power of the dependent variable and its derivatives, while the degree is the highest power to which a derivative is raised.

Given:

Solution:

Here in this question, the order of the differential equation is 2 and the degree of the differential equation is .

In a differential equation, when the dependent variable and their derivatives are only multiplied by constant or independent variable, then the equation is linear.

Here the dependent variable is y and its derivatives are multiplied together with , also y is multiplied by itself. So this equation is non-linear differential equation.

Therefore, Order=2, Degree=3 , Non-linear

Differential Equation exercise 21.1 question 12

Hint:

The order is the highest numbered derivative in the equation with no negative or fractional power of the dependent variable and its derivatives, while the degree is the highest power to which a derivative is raised.Given:

Solution:

Here in this question, the order of the differential equation is 3 and the degree of the differential equation is 1.

In a differential equation, when the dependent variable and their derivatives are only multiplied by constant or independent variable, then the equation is linear.

Here the dependent variable is y and its derivatives are multiplied with itself . So this equation is non-linear differential equation.

Therefore, Order=3 , Degree=1, Non-linear

Differential Equation exercise 21.1 question 13

Hint:

The order is the highest numbered derivative in the equation with no negative or fractional power of the dependent variable and its derivatives, while the degree is the highest power to which a derivative is raised.

Given:

Solution:

The above equation can be written as

Here in this question, the order of the differential equation is 1 and the degree of the differential equation is 1.

In a differential equation, when the dependent variable and their derivatives are only multiplied by constant or independent variable, then the equation is linear.

Here the dependent variable is y and the term is multiplied by y and also y is multiplied by itself. So this equation is non-linear differential equation.

Therefore, Order=1, Degree=1, Non-linear

Differential Equation exercise 21.1 question 14

Hint:

The order is the highest numbered derivative in the equation with no negative or fractional power of the dependent variable and its derivatives, while the degree is the highest power to which a derivative is raised.

Given:

Solution:

The above equation can be written as

Since the power of y cannot be rational so squaring on both sides

Here in this question, the order of the differential equation is 1 and the degree of the differential equation is 2.

In a differential equation, when the dependent variable and their derivatives are only multiplied by constant or independent variable, then the equation is linear.

Here the dependent variable is y and the term is multiplied by itself. So this equation is non-linear differential equation.

Therefore, Order=1, Degree=2, Non-linear

Differential Equation exercise 21.1 question 15

Answer:

Order=2, Degree=3, Non- linearHint:

The order is the highest numbered derivative in the equation with no negative or fractional power of the dependent variable and its derivatives, while the degree is the highest power to which a derivative is raised.

Given:

Solution:

Since the power of is not rational we need to make it rational.

So cubing on both sides, we get

Here in this question, the order of the differential equation is 2 and the degree of the differential equation is 3.

In a differential equation, when the dependent variable and their derivatives are only multiplied by constant or independent variable, then the equation is linear.

Here the dependent variable is y and the term is multiplied by itself. So this equation is non-linear differential equation.

Therefore, Order=2, Degree=3, Non-linear

Differential Equation exercise 21.1 question 17

Hint:

The order is the highest numbered derivative in the equation with no negative or fractional power of the dependent variable and its derivatives, while the degree is the highest power to which a derivative is raised.

Given:

Solution:

Since the equation has rational powers, we need to remove them.

So squaring both sides, we get

Here in this question, the order of the differential equation is 2 and the degree of the differential equation is 2 .

In a differential equation, when the dependent variable and their derivatives are only multiplied by constant or independent variable, then the equation is linear.

Here the dependent variable is y and the term is multiplied by itself. So this equation is non-linear differential equation.

Therefore, Order=2, Degree=2, Non-linear

Differential Equation exercise 21.1 question 18

Hint:

The order is the highest numbered derivative in the equation with no negative or fractional power of the dependent variable and its derivatives, while the degree is the highest power to which a derivative is raised.

Given:

Solution:

First of all, we will rearrange the above equation as follows

Since the equation has rational powers, we need to remove them.

So squaring both sides, we get

Here in this question, the order of the differential equation is 1 and the degree of the differential equation is 2.

In a differential equation, when the dependent variable and their derivatives are only multiplied by constant or independent variable, then the equation is linear.

Here the dependent variable is y and the term is multiplied by itself. So this equation is non-linear differential equation.

Therefore, Order=1, Degree=2, Non-linear

Differential Equation exercise 21.1 question 19

Hint:

The order is the highest numbered derivative in the equation with no negative or fractional power of the dependent variable and its derivatives, while the degree is the highest power to which a derivative is raised.

Given:

where

Solution:

First of all, we will rearrange the above equation as follows

Here we have substituted the value of and taken out from the root. Since the equation has rational powers, we need to remove them.

So squaring both sides, we get

Here in this question, the order of the differential equation is 1 and the degree of the differential equation is 2.

In a differential equation, when the dependent variable and their derivatives are only multiplied by constant or independent variable, then the equation is linear.

Here the dependent variable is y and the term is multiplied by itself. So this equation is non-linear differential equation.

Therefore, Order=1, Degree=2, Non-linear

Differential Equation exercise 21.1 question 20

Hint:

The order is the highest numbered derivative in the equation with no negative or fractional power of the dependent variable and its derivatives, while the degree is the highest power to which a derivative is raised.

Given:

Solution:

Concept of the question

So the equation becomes as follows,

Here in this question, the order of the differential equation is 1 and the degree of the differential equation is 1.

In a differential equation, when the dependent variable and their derivatives are only multiplied by constant or independent variable, then the equation is linear.

Here the dependent variable is y and the term y is multiplied by itself. So this equation is non-linear differential equation.

Therefore, Order=1, Degree=1, Non-linear

Differential Equation exercise 21.1 question 21

Hint:

The order is the highest numbered derivative in the equation with no negative or fractional power of the dependent variable and its derivatives, while the degree is the highest power to which a derivative is raised.

Given:

Solution:

On solving the equation,

Here in this question, the order of the differential equation is 2 and the degree of the differential equation is 1.

In a differential equation, when the dependent variable and their derivatives are only multiplied by constant or independent variable, then the equation is linear.

Here the dependent variable is y and the term is multiplied by itself. So this equation is non-linear differential equation.

Therefore, Order=2, Degree=1, Non-linear

Differential Equation exercise 21.1 question 22

Hint:

The order is the highest numbered derivative in the equation with no negative or fractional power of the dependent variable and its derivatives, while the degree is the highest power to which a derivative is raised.

Given:

Solution:

Concept of the question

So in this question, x of is replaced by which means that the power of is not defined as it approaches to infinity by the above formula.

Here in this question, the order of the differential equation is 2 and the degree of the differential equation is not defined.

In a differential equation, when the dependent variable and their derivatives are only multiplied by constant or independent variable, then the equation is linear.

Here the dependent variable is 2 and the term is multiplied by itself. So this equation is non-linear differential equation.

Therefore, Order=2, Degree = Not defined, Non- linear

Differential Equation exercise 21.1 question 23

Answer:

Order=2, Degree=2 , Non- linearHint:

The order is the highest numbered derivative in the equation with no negative or fractional power of the dependent variable and its derivatives, while the degree is the highest power to which a derivative is raised.

Given:

Solution:

Concept of the question

So in this question, x of is replaced by y which means that the power of y is not defined as it approaches to infinity by the above formula.

Here in this question, the order of the differential equation is 2 and the degree of the differential equation is not defined.

In a differential equation, when the dependent variable and their derivatives are only multiplied by constant or independent variable, then the equation is linear.

Here the dependent variable is y and the term y is multiplied by itself. So this equation is non-linear differential equation.

Therefore, Order=2, Degree=2, Non- linear

Differential Equation exercise 21.1 question 24

Answer:

Order=2, Degree=1, linearHint:

The order is the highest numbered derivative in the equation with no negative or fractional power of the dependent variable and its derivatives, while the degree is the highest power to which a derivative is raised.

Given:

Solution:

Here in this question, the order of the differential equation is 2 and the degree of the differential equation is 1.

In a differential equation, when the dependent variable and their derivatives are only multiplied by constant or independent variable, then the equation is linear.

Here the dependent variable is y and the term is multiplied with x and 5 both. So this equation is linear differential equation.

Therefore, Order=2, Degree=1, linear

Differential Equation exercise 21.1 question 25

Hint:

The order is the highest numbered derivative in the equation with no negative or fractional power of the dependent variable and its derivatives, while the degree is the highest power to which a derivative is raised.

Given:

Solution:

Concept of the question

So in this question, x of is replaced by y which means that the power of y is not defined as it approaches to infinity by the above formula.

Here in this question, the order of the differential equation is 3 and the degree of the differential equation is 1.

In a differential equation, when the dependent variable and their derivatives are only multiplied by constant or independent variable, then the equation is linear.

Here the dependent variable is y and the term y is multiplied by itself. So this equation is non-linear differential equation.

Therefore, Order=3, Degree=1 , Non- linear

Differential Equation exercise 21.1 question 26

Answer:

Order=2, Degree-Not defined , Non- linearHint:

The order is the highest numbered derivative in the equation with no negative or fractional power of the dependent variable and its derivatives, while the degree is the highest power to which a derivative is raised.

Given:

Solution:

Concept of the question

For the degree to be defined of any differential equation, the equation must be expressible in the form of a polynomial.

But in this question the degree of the differential equation is not defined because the term on the right hand side is not expressible in the term of a polynomial.

Here in this question, the order of the differential equation is 2 and the degree of the differential equation is not defined.

Since the degree of the equation is not defined, the equation is non-linear.

Therefore, Order=2, Degree=Not defined, Non- linear

Differential Equation exercise 21.1 question 27

Answer:

Order=1, Degree=3, Non- linearHint:

The order is the highest numbered derivative in the equation with no negative or fractional power of the dependent variable and its derivatives, while the degree is the highest power to which a derivative is raised.

Given:

Solution:

Here in this question, the order of the differential equation is 1 and the degree of the differential equation is 3.

In a differential equation, when the dependent variable and their derivatives are only multiplied by constant or independent variable, then the equation is linear.

Here the dependent variable is y and the term is multiplied with itself. So this equation is non-linear differential equation.

Therefore, Order=1, Degree=3, Non- linear

Class 12 RD Sharma chapter 21 exercise 21.1 is prepared by a team of experts to help students score good marks in their exams. This material contains questions and answers in the same place, which makes it convenient for students for preparation and revision. This material follows the CBSE syllabus and is updated to the latest version of the book. This means that it contains questions from the newest addition of the RD Sharma maths book.

RD Sharma class 12 solutions chapter 21 exercise 21.1 can be accessed through Career360'sCareer360's website. The entire material is available online, which makes it very convenient for students to prepare. Students can use this material as a guide for their textbook and refer to it if they have any doubts. As RD Sharma is a widely used book, the questions from this material might appear in their exams.

RD Sharma Class 12th Exercise 21.1 Chapter 21 is the best material to learn about the chapter and practice well. It contains step-by-step solutions which make it easier to understand even for students who are weak in maths.

RD Sharma class 12 chapter 21 exercise 21.1 material is available for free through Career360'sCareer360's website. Students can take advantage of RD Sharma Class 12th Exercise 21.1 by studying from it and scoring good exams.

- 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

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Download E-book1. Where can students get the RD Sharma class 12th exercise 21.1 Solutions?

RD Sharma Class 12th Exercise 21.1 Chapter 21 material can be accessed through Career360’s website by searching the book name and exercise number.

2. Who can use RD Sharma class 12 chapter 21 exercise 21.1?

Class 12 Maths RD Sharma Chapter 21 material is explicitly made for CBSE students who want to gain more knowledge and score better marks in exams.

3. Does the RD Sharma Class 12 Maths Solutions Chapter 21 material help score good marks?

The Class 12 RD Sharma chapter 21 exercise 21.1 solution follows the CBSE syllabus and covers all topics. It can help students score good marks in exams.

4. What is the cost of class 12 RD Sharma chapter 21 material?

The Class 12 RD Sharma chapter 21 exercise 21.1.material is free for students through Career360’s website.

5. Can I solve NCERT questions after preparing this material?

As RD Sharma and NCERT books have the same concepts, students can solve them after referring to this material.

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