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RD Sharma Class 12 Solutions Chapter 22 - Differential Equations (Ex 22.8) Exercise 22.8 - Free PDF

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Last updated date: 22nd Mar 2024
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MVSAT 2024

RD Sharma Solutions to Class 12

Free PDF Download of RD Sharma Class 12 Solutions Chapter 22 - Differential Equations Exercise 22.8 solved by Expert Mathematics Teachers on Vedantu.com. All Chapter 22 - Differential Equations Ex 22.8 Questions with Solutions for RD Sharma Class 12 Maths to help you to revise the complete Syllabus and Score More marks. Register for online coaching for IIT JEE (Mains & Advanced) and other engineering entrance exams.

For students taking their Class 12 math exam, RD Sharma Class 12 Solutions Chapter 22 is a bible. This PDF's solutions are organised in a student-friendly manner. Students can use these solutions to help them prepare for their maths exams. Experts that work with us have made it their mission to ensure that pupils face no problems comprehending this exercise. The solutions are presented in a step-by-step format for easy and quick understanding. So, let's get started by learning the fundamentals of the chapter.

Competitive Exams after 12th Science

Topics Covered Under RD Sharma Class 12 Solutions Chapter 22 - Differential Equations

Differential Equation: A differential equation is an equation that contains an independent variable, a dependent variable, derivatives of the dependent variable concerning the independent variable, and a constant.

Ordinary Differential Equation: An ordinary differential equation involves derivatives of the dependent variable with regard to only one independent variable.

A differential equation can be created from any given relationship between the dependent and independent variables by differentiating it with respect to the independent variable and removing any arbitrary constants involved.

The order of a differential equation is defined as the highest order derivative of the dependent variable with respect to the independent variable in the given differential equation.

What is the Degree of a Differential Equation?

The highest exponent of the highest order derivative is called the degree of a differential equation if each derivative's exponent is a non-negative integer and the unknown variable in the differential equation is a non-negative integer. 

  • A differential equation's order and degree (if defined) are always positive integers.

  •  The differential equation is a derivative polynomial equation.

  • The degree of a differential equation is not specified if it is not a polynomial equation in its derivatives.

FAQs on RD Sharma Class 12 Solutions Chapter 22 - Differential Equations (Ex 22.8) Exercise 22.8 - Free PDF

1. What is a differential equation?

A differential equation is an equation that contains an independent variable, a dependent variable, derivatives of the dependent variable concerning the independent variable, and a constant. There are many types of differential equations. Find them listed below:

  • Ordinary Differential Equations

  • Partial Differential Equations

  • Linear Differential Equations

  • Nonlinear differential equations

  • Homogeneous Differential Equations

  • Nonhomogeneous Differential Equations

To simulate the behaviour of complex systems, differential equations are used. The mathematical theory of differential equations evolved in tandem with the sciences that gave rise to the equations and where the results were applied.

2. How is RD Sharma Class 12 Chapter 22 - Differential Equations (EX - 22.8) helpful for me?

The RD Sharma Class 12 Chapter 22 - Differential Equations is helpful for you as it will help you further clear your concepts. The exercise includes a very thorough explanation of each problem in an understandable manner. Referring to these solutions will help you assess where you’re lacking. And if not, then it will help you gain confidence in your preparation. Only NCERT isn’t enough when you’re preparing to take your class twelfth Maths exam. So, RD Sharma Solutions are here to help you. 

3. What is a partial differential equation?

A partial differential equation (or PDE for short) is a mathematical equation having two or more independent variables, an unknown function (depending on those variables), and partial derivatives of the unknown function concerning the independent variables. The highest derivative involved in a partial differential equation determines its order. When a partial differential equation is substituted into it, a solution (or a particular solution) is a function that solves the equation or, in other words, turns it into an identity. If a solution contains all particular solutions to the problem in question, it is referred to as generic.

4. Where can I find other resources to learn more about the chapter differential equations?

You can find many other resources other than RD Sharma Solutions on the website or app. These resources charge no fee at all. And can be availed by anyone at any point in time. The resources include last years’ question papers, comprehensive notes, practice sheets, RD Sharma Solutions for other exercises. You can also contact us with your problems and queries and our experts will get back to you with solutions. These resources will definitely help you ace your class twelfth math board exam.

5. What are the applications of differential equations?

Differential equations are used in a variety of domains, including applied mathematics, science, and engineering. They are used to solve a variety of real-world challenges in addition to technical applications. Let's look at some real-time differential equation applications.

  • Differential equations are used to describe the growth and decay of various exponential functions.

  • They can also be used to describe how a return on investment changes over time.

  • They're employed in a medical study to model cancer growth and disease spread across the body.

  • It can also be used to describe the movement of electricity.

  • They assist economists in determining the most effective investment options.

  •  These equations can also be used to describe the motion of waves or a pendulum.