NCERT Solutions for Maths Class 12 Exercise 9.3

# NCERT Solutions for Maths Class 12 Exercise 9.3

Hello Students. In this post, you will find the complete NCERT Solutions for Maths Class 12 Exercise 9.3.

You can download the PDF of NCERT Books Maths Chapter 9 for your easy reference while studying NCERT Solutions for Maths Class 12 Exercise 9.3.

All the schools affiliated with CBSE, follow the NCERT books for all subjects. You can check your syllabus from NCERT Syllabus for Mathematics Class 12.

If you want to recall All Maths Formulas for Class 12, you can find it by clicking this link.

If you want to recall All Maths Formulas for Class 11, you can find it by clicking this link.

NCERT Solutions for Maths Class 12 Exercise 9.1

NCERT Solutions for Maths Class 12 Exercise 9.2

NCERT Solutions for Maths Class 12 Exercise 9.4

NCERT Solutions for Maths Class 12 Exercise 9.5

## NCERT Solutions for Maths Class 12 Exercise 9.3

For each of the following differential equation in Exercises 1 to 10, find the general solution:

Maths Class 12 Ex 9.3 Question 1.

Solution:

Maths Class 12 Ex 9.3 Question 2.

Solution:

Maths Class 12 Ex 9.3 Question 3.

Solution:

Maths Class 12 Ex 9.3 Question 4.

sec² x tan y dx + sec² y tan x dy = 0

Solution:

We have, sec² x tan y dx + sec² y tan x dy = 0

Maths Class 12 Ex 9.3 Question 5.

Solution:

Maths Class 12 Ex 9.3 Question 6.

Solution:

Maths Class 12 Ex 9.3 Question 7.

y log y dx – x dy = 0

Solution:

We have, y log y dx – x dy = 0
dy/y log y = dx/x         … (i)
Integrating equation (i) on both sides, we get

Maths Class 12 Ex 9.3 Question 8.

Solution:

Maths Class 12 Ex 9.3 Question 9.

Solution:

Maths Class 12 Ex 9.3 Question 10.

Solution:

which is the required solution.

For each of the following differential equations in Exercises 11 to 14, find a particular solution satisfying the given condition:

Maths Class 12 Ex 9.3 Question 11.

Solution:

Maths Class 12 Ex 9.3 Question 12.

Solution:

Maths Class 12 Ex 9.3 Question 13.

Solution:

Maths Class 12 Ex 9.3 Question 14.

Solution:

Maths Class 12 Ex 9.3 Question 15.

Find the equation of the curve passing through the point (0, 0) and whose differential equation is y’ = ex sin x.

Solution:

Maths Class 12 Ex 9.3 Question 16.

For the differential equation , find the solution curve passing through the point (1, –1).

Solution:

The given differential equation is
or xy dy = (x + 2) (y + 2) dx

Maths Class 12 Ex 9.3 Question 17.

Find the equation of a curve passing through the point (0, –2) given that at any point (xy) on the curve, the product of the slope of its tangent and y-coordinate of the point is equal to the x-coordinate of the point.

Solution:

Maths Class 12 Ex 9.3 Question 18.

At any point (xy) of a curve, the slope of the tangent is twice the slope of the line segment joining the point of contact to the point (–4, –3). Find the equation of the curve given that it passes through (–2, 1).

Solution:

Slope of the tangent to the curve = dy/dx
Slope of the line joining (xy) and (–4, –3)

Maths Class 12 Ex 9.3 Question 19.

The volume of a 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 t seconds.

Solution:

Let v be volume of the balloon.

Maths Class 12 Ex 9.3 Question 20.

In a bank, principal increases continuously at the rate of r% per year. Find the value of r if Rs 100 double itself in 10 years (log 2 = 0.6931).

Solution:

Let P be the principal at any time t.
According to the problem,

Maths Class 12 Ex 9.3 Question 21.

In a bank, principal increases continuously at the rate of 5% per year. An amount of Rs 1000 is deposited with this bank, how much will it worth after 10 years (e0.5 = 1.648).

Solution:

Maths Class 12 Ex 9.3 Question 22.

In a culture, the bacteria count is 1,00,000. The number is increased by 10% in 2 hours. In how many hours will the count reach 2,00,000, if the rate of growth of bacteria is proportional to the number present?

Solution:

Let y denote the number of bacteria at any instant t.

According to the question,

Maths Class 12 Ex 9.3 Question 23.

The general solution of the differential equation  is

(A)  ex + e-y = C
(B)  ex + ey = C
(C)  e-x + ey = C
(D)  e-x + e-y = C

Solution:

Hence, the correct answer is option (A).