# RD SHARMA Solutions for Class 12-science Maths Chapter 22 - Differential Equations

## Chapter 22 - Differential Equations Exercise Ex. 22.1

Determine the order and degree of the following differential equations. State also whether they are linear or non-linear.

The order of a differential equation is the order of the highest order derivative appearing in the equation.

The degree of a differential equation is the degree of the highest order derivative.

Consider the given differential equation

In the above equation, the order of the highest order derivative is 1.

So the differential equation is of order 1.

In the above differential equation, the power of the highest order derivative is 3.

Hence, it is a differential equation of degree 3.

Since the degree of the above differential equation is 3, more than one, it is a non-linear differential equation.

## Chapter 22 - Differential Equations Exercise Ex. 22.2

Form the differential equation having y = (sin^{-1}x)^{2} + A cos^{ -1} x + B, where A and B are arbitrary constants, as its general solution.

Represent the following family of curves by forming the corresponding differential equation (a,b being parameters):

x^{2 } + (y - b)^{2} = 1

## Chapter 22 - Differential Equations Exercise Ex. 22.3

show that y = ae^{2}x + be^{-x} is a solution of the differential equation

Verify that y = + b is a solution of the differential equation

Show that y = e^{x}(A cos x + B sin x) is the solution of the differential equation

Show that y = e^{-x} + ax + b is solution of the differential equation

For the following differential equation verify that the accompanying function is a solution in the mentioned domain (a, b are parameters)

## Chapter 22 - Differential Equations Exercise Ex. 22.4

For the following initial value problem verify that the accompanying function is a solution:

## Chapter 22 - Differential Equations Exercise Ex. 22.5

Solve the following differential equation:

(sin x + cos x)dy + (cos x - sin x) dx = 0

Solve the following differential equation:

Solve the following differential equation

solve the following differential equation

## Chapter 22 - Differential Equations Exercise Ex. 22.6

Solve the following differential equation:

Solve the following differential equation:

## Chapter 22 - Differential Equations Exercise Ex. 22.7

Solve the following differential equation:

Solve the following differential equation:

Solve the following differential equation:

ye^{x}^{/y} dx = (xe^{x}^{/y} + y^{2}) dy, y ¹ 0

(1 + y^{2}) tan^{-1} x dx + 2y (1 + x^{2})dy = 0

Solve the following initial value problem

=1 + x^{2} + y^{2} + x^{2}y^{2}, y(0) = 1

Solve the following initial value problem

Find the particular solution of e= x + 1, given that y = 3 when x = 0.

Find the equation of a curve passing through the point (0,0) and whose differential equation is

The volume of spherical balloon being inflated changes at a constant rate. If initially its radius is 3 units and after 3 seconds it is 6 units. Find the radius of balloon after after t seconds.

in a bank,principal increases continuously at the rate of r% per year. Find The value of r if Rs 100 doubles itself in 10 years (log_{e} 2 = 0.6931).

Let p, t and represent the principal, time, and rate of interest respectively.

It is given that the principal increases continuously at the rate of r% per year.

Integrating both side, we get:

## Chapter 22 - Differential Equations Exercise Ex. 22.8

Solve the following differential equation.

## Chapter 22 - Differential Equations Exercise Ex. 22.9

Solve the following differential equation:

Solve the following differential equation:

Solve the following initial value problem

Solve the following initial value problem

Solve the following initial value poblem

Solve the following differential equation:

Solve the following initial value problem

Solve the following initial value problem

## Chapter 22 - Differential Equations Exercise Ex. 22.10

Solve the following differential equation:

Solve the following differential equation:

Solve the following initial value problem:

Solve the following initial value problem

dy = cos x (2 - y cosec x) dx

Solve the differential equation

## Chapter 22 - Differential Equations Exercise Ex. 22.11