## NCERT solutions for Class 12 Maths Chapter 9

### NCERT Solutions for Class 12 Maths Chapter 9 Solutions in English and Hindi Medium

Class: 12 | Maths |

Chapter: 9 | Differential Equations |

Contents: | NCERT Solutions in Hindi and English Medium |

### 12th Maths Chapter 9 Solutions

NCERT solutions for class 12 Maths chapter 9 Differential equations all exercises with miscellaneous exercise are given below to download in PDF format free. NCERT Books and Offline apps are updated according to latest CBSE Syllabus. Ask your doubts related to NIOS and CBSE Board through discussion forum and reply the questions asked by others.

### Class 12 Maths Chapter 9 Solutions in PDF

#### Term related to Differential Equation

1. Differential Equation: An algebraic equation containing differential terms is called differential equation.

2. Order of Differential equation: The highest order derivative present in any differential equation, determines the order of the differential equation.

3. Degree of Differential equation: If the differential equations are simplified so that the differential coefficients present in it are not in the irrational form, then the power of the highest order derivatives determines the degree of the differential equation.

4. General Solution: The solution which contains a number of arbitrary constants equal to the order of the equation is called the general solution or complete integral of the differential equation.

5. Particular Solution: Solution obtained from the general solution by given particular values to the constants are called particular solution.

##### Questions from Board Papers

1. Solve the differential equation x(dy/dx) + y = x cos x + sin x, given that y = 1 when x = π/2. [Delhi 2017]

2. Find the particular solution of the differential equation (1 – y²) (1 + log x)dx + 2xy dy = 0, given that y = 0 when x = 1. [Delhi 2016]

3. Write the differential equation obtained by eliminating the arbitrary constant C in the equation representing the family of curves xy = C cos x. [Delhi 2015C]

4. Find the particular solution of the differential equation x)dy/dx) + y – x + xy cot x = 0, given that when x = π/2, y = 0. [Delhi 2015C]

5. Solve the differential equation x² dy + (xy + y²) dx = 0, given y = 1, when x = 1. [Delhi 2015C]

6. Solve the differential equation: (〖tan〗^(-1) y-x)dy=(1+y²)dx [Delhi 2015]

7. Find the particular solution of the differential equation dy/dx=xy/(x²+y²) , given that y = 1 when x = 0.

### Important Questions on 12th Maths Chapter 9

What is a differential equation?

An equation involving derivative (derivatives) of the dependent variable with respect to independent variable (variables) is called a differential equation.

What is an ordinary differential equation?

A differential equation involving derivatives of the dependent variable with respect to only one independent variable is called an ordinary differential equation.

What do you meant by a partial differential equation?

A differential equation involving derivatives with respect to more than one independent variables is called a partial differential equation.

What is order in Differential equation?

Order of a differential equation is the order of the highest order derivative occurring in the differential equation.

What is degree in Differential Equations?

Degree of a differential equation is defined if it is a polynomial equation in its derivatives. Degree (when defined) of a differential equation is the highest power (positive integer only) of the highest order derivative in it.

What is different between a general solutions and a particular solutions.

A relation between involved variables, which satisfy the given differential equation is called its solution. The solution which contains as many arbitrary constants as the order of the differential equation is called the general solution and the solution free from arbitrary constants is called particular solution.