# RD Sharma Class 12 Chapter 22 Solutions (Differential Equations)

RD Sharma Class 12 Maths Solutions Chapter 22 Differential Equations will teach you about the Formation of the Differential equation, differential equation definition, the order of differential equation, degree of a differential equation, linear and nonlinear differential equation, solution of a differential equation, initial value problems, general form of a first-order first-degree differential equation, Geometrical interpretation of the differential equations of the first order and first degree, solution of the first order and first-degree differential equations, methods of solving a first-order first degree, differential equations of the type dy/dx = f(x), differential equations of the type dy/dx = f(y), equations in variable separable form, equations reducible to variable separable form, homogeneous differential equations, Linear differential equations, linear differential equations of the form dx/dy + Rex = S, applications of differential equations, on newton’s law of cooling, and more.

The entire chapter consists of 11 exercises and a total of 285 questions. These questions take you into the depth of everything differential equations are about. You’ll also study their applications, how they impact the evaluation and much more. If you practice these questions well, you’ll be ready to appear in your CBSE and engineering entrance examinations with confidence and familiarity of the chapter.

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## Topics discussed in RD Sharma Class 12 Maths Solutions for ‘Differential Equations’

**Differential equation definition**

An equation consisting of a dependent variable, independent variable, and dependent variable’s differential coefficients w.r.t independent variable can be called as a differential equation.

For example dy/dx = 2xy

**Types of differential equations**

- Partial Differential Equations
- Ordinary Differential Equations
- Nonlinear Differential Equations
- Linear Differential Equations
- Nonhomogeneous Differential Equations
- Homogeneous Differential Equations

**Order of differential equation**

An order of a given differential equation will be the higher-order derivative’s order in that equation.

(d2y/dx2) + 3(dy/dx)+2y = ex

Here the highest order derivative will be 2.

**Degree of a differential equation**

Degree of a given differential equation will be the highest order derivative’s degree. This is when the differential coefficients do not contain fractions and radicals.

**Linear and Nonlinear differential equations**

A differential equation can also be called as a linear differential equation if it can be expressed as

Where

Could be the constants or functions of x, independent variable.

**Solution of a differential equation**

In order to find out the solution of a differential equation, you need to know that this solution is a relation between all the variables that are involved. These variables will satisfy the given differential equation. Such type of relation and the derivative you obtain can be substituted in the given differential equation making the left-hand side exactly the same as the right-hand side.

### Discussion of Exercises in RD Sharma Solutions for Class 12 Maths Chapter – Differential Equations

- Exercise 22.1 asks you to apply your learning to determine the order and the degree of the given differential equations. It contains 26 questions in total.
- Exercise 22.2 comprises 19 questions where you’ll be asked to form the differential equation of a curve or a circle or a non-vertical line, etc.
- Exercise 22.3 comprises 21 questions where you will be given a differential equation and you will need to verify that the given value of y is true.
- Exercise 22.4 has initial value problems and a given function. You’ll be required to verify the accompanying function is a solution. This exercise has 9 questions in total.
- Exercise 22.5 contains 26 questions where you will have to solve a given differential equation.
- Exercise 22.6 asks you the methodology to solve the given differential equations based on the type dy/dx = f(y). This exercise has 4 questions.
- Exercise 22.7 has 57 questions where you will need to solve the given differential equations based on equations in variable separable form.
- Exercise 22.8 contains 10 questions based on equations reducible to variable separable form.
- Exercise 22.9 has 38 questions based on homogeneous differential equations.
- Exercise 22.10 comprises 41 questions based on linear differential equations and linear differential equations of the form dx/dy = Rx = S
- Exercise 22.11 has 34 questions based on applications of differential equations like growth and decay, Newton’s law of cooling, Applications of Coordinate Geometry, and more.

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