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# RS Aggarwal Class 12 Chapter 18 Solutions (Differential Equations and Their Formation)

RS Aggarwal Solutions for Class 12 Chapter 18 ‘Differential Equation and their Formation’ are prepared to introduce you and assist you with concepts of Differential Equations in your syllabus. In RS Aggarwal Solutions, You will learn about the formation of Differential Equations. There are various types of differential equations such as homogeneous and non-homogeneous, Linear and nonlinear, Ordinary and Partial which will be discussed in the solutions of RS Aggarwal Class 12 Chapter 18 questions. This topic is of vital importance in your higher studies because of its wide-ranging applications.

There are 3 exercises consisting of 26 questions in total. These exercise questions of Chapter 18 are arranged in such a fashion to aid you to learn the topics gradually in a step by step manner. The questions in RS Aggarwal Class 12 Solutions for Chapter 18 Differential Equation and their formation will aid you to prepare well for the competitive entrance exams such as NEET, JEE etc. to help you move a step ahead towards your dream career. Solving these questions will make you proficient in this topic and all kinds of questions, related to this topic, that recur in the board exams.

We, at Instasolv, keep ourselves updated to the latest CBSE Syllabus and the dynamic trends of the exam pattern. Thus, Instasolv is very reliable when it comes to reference for answers based on the Board pattern. This chapter is very scoring if you grasp the methodology of approaching a question. The solutions at Instasolv are so detailed that they will boost your analytical skills and enhance your marks exponentially in your school exams. To build a robust base for your higher studies, you must keep referring to these solutions of RS Aggarwal Class 12 book for revision.

## Topics Covered in RS Aggarwal Solutions for Chapter 18 – Differential Equations and Their Formation

Introduction:

An equation that contains one or more functions with its derivatives is called a differential equation. The derivatives of the function tell us about the rate of change of a function at a point. It is mainly utilized in fields like physics, engineering, biology, and so on. The primary purpose of the differential equation is the study of solutions that satisfy the equations, and hence the properties of the solutions. One of the simplest ways to solve the differential equation is by using explicit formulae. Here we will talk about the definition, types, methods to solve the differential equation, ordinary differential equations.

Differential Equation Definition:

A differential equation is an equation which contains one or more terms which involve the derivatives of one variable (i.e., dependent variable) with respect to the other variable (i.e., independent variable)

dy/dx=f(x)

where x the independent variable and y is the dependent one.

For example, dy/dx = 5x

Differential Equation Types:

Differential equations are of the following types:

1. Ordinary Differential Equations
2. Partial Differential Equations
3. Linear Differential Equations
4. Non-linear differential equations
5. Homogeneous Differential Equations
6. Non-homogenous Differential Equations

Differential Equations Solutions:

To find the solution of the differential equations, there are two methods to solve differential function.

1. Separation of variables
2. Integrating factor

Ordinary Differential Equation:

A Differential equation that involves a single function and its derivatives is called an ordinary differential equation. It has only one independent variable and may contain one or more of its derivative with respect to the variable.

ODE of nth order has the following general form:

F(x, y, y, …,yn ) = 0

Applications:

Some of the applications of differential equations are:

1. Differential equations describe various exponential growths and decays.
2. They are used to determine the change in investment return over a given time period.
3. They are used in the field of medical science for modelling cancer growth or the spread of disease in the body.
4. The movement of electricity can also be described with the help of it.
5. They help economists in finding optimum investment strategies.

The various other applications in engineering are: ­ heat conduction analysis, in physics it can be used to understand the motion of waves. The ordinary differential equation can be utilized as an application in the engineering field like for finding the relationship between various parts of the bridge.

### Discussion of Exercise Questions of RS Aggarwal Solutions for Class 12 Chapter 18 Differential Equations and Their Formation

1. The exercise solutions in Chapter 18 of RS Aggarwal cover all the topics of Chapter 18.
2. These exercise solutions in the RS Aggarwal Class 12 Chapter 18 require in-depth knowledge of Differential Equations and its types.
3. The questions are both objective type or short answer type, and elaborate long answer type.
4. These RS Aggarwal Solution are strictly based on the latest CBSE guidelines. You can follow them for the revision as well as for the competitive exam preparation.

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