# NCERT Solutions for Class 12 Maths Chapter 9 Differential Equations

NCERT solutions for class 12 Maths chapter 9 exercise 9.1, 9.2, 9.3, 9.4, 9.5, 9.6 & miscellaneous exercises of Differential equations in PDF form to free download. Get the NCERT Solutions of all other subject based on latest CBSE Syllabus for 2019-2020. Download NCERT Solutions Offline Apps which work properly without internet also.

 Class: 12 Subject: Maths – गणित Chapter 9: Differential equations

## NCERT solutions for class 12 Maths chapter 9

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### Assignments for practice

Level 1 Test 1

Level 2 Test 1

Level 3

#### Term related to Differential Equation

• Differential Equation: An algebraic equation containing differential terms is called differential equation.
• Order of Differential equation: The highest order derivative present in any differential equation, determines the order of the differential equation.
• 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.
• 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.
• Particular Solution: Solution obtained from the general solution by given particular values to the constants are called particular solution.

#### Previous Year’s Questions

1. Prove that is the general solution of the differential equation , where C is a parameter. [Delhi 2017]
2. Solve the differential equation x(dy/dx) + y = x cos x + sin x, given that y = 1 when x = π/2. [Delhi 2017]
3. Find the sum of the order and the degree of the following differential equation: [CBSE Sample Paper 2017]
4. Can y = ax + b/a be a solution of the following differential equation? . If no, find the solution of this differential equation. [CBSE Sample Paper 2017]
5. Check whether the following differential equation is homogeneous or not. Find the general solution of the differential equation using substitution y = vx. [CBSE Sample Paper 2017]
6. 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]
7. Find the general solution of the following differential equation: [Delhi 2016]
8. 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]

1. Write the sum of the order and degree of the differential equation. [Delhi 2015C]
2. 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]
3. Solve the differential equation x² dy + (xy + y²) dx = 0, given y = 1, when x = 1. [Delhi 2015C]
4. Solve the differential equation: (〖tan〗^(-1) y-x)dy=(1+y²)dx [Delhi 2015]
5. Find the particular solution of the differential equation dy/dx=xy/(x²+y²) , given that y = 1 when x = 0.

#### 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.

## 2 thoughts on “NCERT Solutions for Class 12 Maths Chapter 9 Differential Equations”

1. Vipul Agrawal says:

Sir, I need solutions of above mentioned Test Paper (Level 1,2,3). From where we can get those solutions.

2. raj says:

sir hindi me solustion uplod kijiye